Hi, I came to US from Mexico. I have pending asylum case with USCIS. I am in TPS right now which will expire next month though it will be renewed till next year.

Anyway I have to travel to Canada asap, so my question is, is it safe to travel to Canada while I have only 1 month left in Advanced Parole Document. What are the risks? Any help will be appreciated. Anyone has traveled abroad while their TPS was about to expire.

I traveled to Nepal with TPS AP for two weeks and came back a week ago. Did not encounter any problems with immigration coming back. My entry point was JFK. After getting my passport checked and finger prints taken at the Visitor Queue, was then directed to a separate room. Had to wait about 15 minutes, the parole officer verified my AP document, stamped it and told me to have a nice day.
That was my experience, in my opinion as long as you do not have a criminal record and all the info on your passport and AP match up perfectly you won't have an issue coming back. There was a lady stuck because her name was spelt wrong way (lastname firstname) on her VISA. I believe she was detained overnight.