I am an employee of one of those big, wealthy companies (henceforth BWC), and believe me, I feel your pain. I already find it great that BWC would let your students publish their research, I can tell you from hard-won experience that this can be quite a struggle once the legal function gets wind of it! (So here is your answer to "is this common?": at my employer, I would not even try to apply for funding for an ex-intern, because I know it would be absolutely hopeless.)
Now, of course we can't tell you who should fund your students' conference travel, there is no objective answer to that. What we can do is discuss the matter itself, and suggest possible ways forward.
First off, funding someone who is not employed any more at BWC is indeed a major pain, for internal and external reasons. This is just something that runs counter to all financial processes in industry. You will pay employees, sure. But if someone is not even working for you any more, then what you would need to do is to have a highly non-standard contract with them specifying payment to third parties (i.e., the travel cost), but no payment to the ex-employee themselves. The rationale would be that this is a benefit to BWC, sure. But then all kinds of regulatory issues crop up: if there is a benefit, isn't the employee again working for the company? If so, are you running afoul of minimum wage laws, because you are not paying them anything? What about benefits? What if something happens on that trip and insurance is claimed? And all this becomes even more nightmarish if the travel happens in a different year than the original contract...
Bottom line: while this issue is indeed infuriating, it is not simply because of obstinacy, laziness or greed on the side of BWC. Paying for your student raises real issues at BWC, which would necessitate a major effort to address, and conversely probably do not happen often enough to set up a dedicated process.
OK, so what can you do about this?
I would say that understanding the issues up front is key. Discuss this issue with any student before they apply to internships. Better to have this out in the open before they invest a lot of time, which may indeed go to waste in terms of a publication.
If you have an onboarding information pack for new Ph.D. students, you may want to put this info in there. If you discuss it in a meeting, send them an email afterwards so you have something on file in case anyone misremembers this. Recall the conversation (e.g., sending out that email) when they do start on their internship.
The most realistic solution would probably be for the student to pay for the conference themselves. Yes, this sounds harsh. But they will presumably be paid at BWC, and they can then decide themselves if they want to pull down, say, 2000 USD per month for three months, or essentially get 1000 USD per month plus 3000 USD altogether for conference costs. Sure, this is a more painful way of thinking than having a contract that up front says "1000 USD per month plus a budget of 3000 USD for a conference" - a question of framing. The key thing, again, is having this conversation with them before they invest their time.
Of course, BWC may actually not be paying that much. Maybe your student is working at a PNP (poor non-profit) at a nominal wage. In which case, there will be even less money from PNP to fund a conference, and tapping other sources of funds (see bottom point) becomes even more important. In this case, "I worked at PNP, and there are no funds there" is a good argument in applying for a grant.
However, note that "self-paying" out of their intern salary at least keeps the door open to apply for other funding. They can with a clear conscience tick the box "I do not have other sources of funding". There may be additional funds at your university for conference trips, or the conference may have travel grants, etc. These are still an option for your student. (And of course, people will still grumble about having to subsidize the student, rather than BWC paying - but per above, BWC has already paid the student an amount that could probably be considered as covering a conference.)
Finally, a word to you as the professor: while it is natural and commendable that you feel responsible for your students, your research and travel funds are limited, and you need to draw a line somewhere. You would presumably not fund some other Ph.D. student in your school whose research does not overlap with yours, either. So do not feel bad about declining a request for funding. Just make this clear from the get-go, and help your student with applying for grants.
Bottom line: discuss this issue with your students before they embark on the internship, and have a plan ready so they know what they are getting into, and ideally already know where to apply for funding.
