I am very sorry this is happening. But do remember that the pension, when it comes, will have some backpay involved, in other words, it will pay you based on the week you first applied. Like Social Security retirement, you do not get the pay until after the full month has passed that you applied for. You do have money coming to you later for this month. And remember, even if you had to go out and borrow money to live on this month, it's better than getting overpaid and having to pay back unemployment benefits with penalties and having the possibility of being prosecuted over your head because you've actually committed fraud.
And do remember that concerning your unemployment benefits, you need to make certifications for benefits and job searches all this month too, get these weeks between now and December applied for just as if you were being paid for them, because when your situation is looked at by the unemployment system and a determination is made, if you were entitled to pay for these weeks when you were not receiving benefits, you will not receive this backpay unless you have filed for the weeks in the appropriate manner. It if turns out you are not eligible for them, you'll not be overpaid. If it turns out you're eligible for part of them, you'll already have that in place and it will be some more backpay money coming in (after they've taken care of any possible overpayments that have already been made.)
