The hurdle is to get accepted to another program. If you can be accepted then nothing else will stand in the way, though you may have to convince a new advisor that the reasons for the earlier failure to finish are reasonable.
A three year limitation on a degree isn't actually very compatible with the realities of serious research. It can't be scheduled. Some problems seem to be amenable to solution but turn out not to be. Some researchers spend many many years on a problem and don't come to a solution. I think Einstein spent about ten years to gain insight into special relativity.
And, you don't know why it didn't get done in four years. It might have been the problem itself. It might have been health, or having a child. It might have been an advisor who insisted on solving an impossible problem. It could have been any of a hundred other things. She "didn't" finish he program. That may not say anything about her skill. Your use of "couldn't" is pejorative. It may not apply.
I was once in a similar situation, moved to a better place, got a better advisor and finished with the respect of the faculty. It certainly isn't impossible. I had a sort of sponsor who helped me make the move. He was a mentor, but was in a different subfield, so not my advisor. But he saw promise and was happy to say so.