Can I claim foreign tax credit carryovers for past years even though I didn't file taxes during those years?

You’d be better off with an accountant for this question.

How can you have a tax credit form if you didn’t file? You must have received the form for filing something somewhere. You need to contact an accountant familiar with reciprocal tax agreements between what ever two countries you are talking about. If it is a loss that can be carried forward to another year, I would say, yes, you could, but it all depends on the countries and what the rules are for where you are. I can not look this up for you if you are in the US. US tax laws make me want to jump off a tall building.