When terminating an employee, can I tell them the company will not fight unemployment filing?

Yes. In fact, I often recommend this course of action to my clients when they are firing someone for poor performance or for some other reason such as not being quite as capable in the role as desired.

If you are firing someone for other than egregious behavior (such as a truly terrible attendance record or for stealing, for example) you would most likely not prevail if you did "fight" the terminated employee collecting unemployment.

So, why not defuse the situation and just say that the company will acquiesce to the terminated employee being paid her unemployment benefits? It is also a kind thing to do, as long as it is true.

Being fired is stressful enough, if you can make it a tad less so, why not do it?