To get a feel for this situation from the student's point of view, I suggest reading questions such as Changing PhD programs: should I submit a recommendation letter from my old advisor if it's not purely positive?, Incompatibility with the PhD advisor, Switch PhD program: how to contact possible PhD advisors when already enrolled in PhD program?, and many others.

The decision to try to switch programs is a difficult one for the student. They may be worried about harming their relationship with the current advisor if the move does not work out. From this point of view, contacting the advisor, rather than the student, would be like calling a job applicant's current employer.

Although if they asked here they would probably be advised against it, there may be a temptation to just not mention the current PhD program other than to the extent that they have worked as a research assistant.

The key question you need to ask both the students and yourself is "What would be different about my project compared to your current one?". Of course, there are no guarantees, except that you will not be able to get through a reasonably interesting life without embarrassment.

For example, see How to explain in PhD interview about leaving current PhD due to lack of funding?. If you have good funding, and the student is switching because of lack of funding, there is no reason to expect them to be particularly likely to leave.

The OP for that question wrote "I did not mention my current PhD in CV, and just wrote about my working experience in the last 1.5 year.". I have no idea why students do that, but it seems to be a common urge. Many questions either discuss the advisability of not mentioning incomplete degrees when applying for a PhD program, or are trying to deal afterwards with the consequences of not mentioning them.

To get a feel for this situation from the student's point of view, I suggest reading questions such as Changing PhD programs: should I submit a recommendation letter from my old advisor if it's not purely positive?, Incompatibility with the PhD advisor, Switch PhD program: how to contact possible PhD advisors when already enrolled in PhD program?, and many others.

The decision to try to switch programs is a difficult one for the student. They may be worried about harming their relationship with the current advisor if the move does not work out. From this point of view, contacting the advisor, rather than the student, would be like calling a job applicant's current employer.

Although if they asked here they would probably be advised against it, there may be a temptation to just not mention the current PhD program other than to the extent that they have worked as a research assistant.

The key question you need to ask both the students and yourself is "What would be different about my project compared to your current one?". Of course, there are no guarantees, except that you will not be able to get through a reasonably interesting life without embarrassment.

For example, see How to explain in PhD interview about leaving current PhD due to lack of funding?. If you have good funding, and the student is switching because of lack of funding, there is no reason to expect them to be particularly likely to leave.

The OP for that question wrote "I did not mention my current PhD in CV, and just wrote about my working experience in the last 1.5 year.". I have no idea why students do that, but it seems to be a common urge. Many questions either discuss the advisability of not mentioning incomplete degrees when applying for a PhD program, or are trying to deal afterwards with the consequences of not mentioning them.

To get a feel for this situation from the student's point of view, I suggest reading questions such as Changing PhD programs: should I submit a recommendation letter from my old advisor if it's not purely positive?, Incompatibility with the PhD advisor, Switch PhD program: how to contact possible PhD advisors when already enrolled in PhD program?, and many others.

The decision to try to switch programs is a difficult one for the student. They may be worried about harming their relationship with the current advisor if the move does not work out. From this point of view, contacting the advisor, rather than the student, would be like calling a job applicant's current employer.

Although if they asked here they would probably be advised against it, there may be a temptation to just not mention the current PhD program other than to the extent that they have worked as a research assistant.

To get a feel for this situation from the student's point of view, I suggest reading questions such as Changing PhD programs: should I submit a recommendation letter from my old advisor if it's not purely positive?, Incompatibility with the PhD advisor, Switch PhD program: how to contact possible PhD advisors when already enrolled in PhD program?, and many others.

The decision to try to switch programs is a difficult one for the student. They may be worried about harming their relationship with the current advisor if the move does not work out. From this point of view, contacting the advisor, rather than the student, would be like calling a job applicant's current employer.

Although if they asked here they would probably be advised against it, there may be a temptation to just not mention the current PhD program other than to the extent that they have worked as a research assistant.

The key question you need to ask both the students and yourself is "What would be different about my project compared to your current one?". Of course, there are no guarantees, except that you will not be able to get through a reasonably interesting life without embarrassment.

For example, see How to explain in PhD interview about leaving current PhD due to lack of funding?. If you have good funding, and the student is switching because of lack of funding, there is no reason to expect them to be particularly likely to leave.

The OP for that question wrote "I did not mention my current PhD in CV, and just wrote about my working experience in the last 1.5 year.". I have no idea why students do that, but it seems to be a common urge. Many questions either discuss the advisability of not mentioning incomplete degrees when applying for a PhD program, or are trying to deal afterwards with the consequences of not mentioning them.