Will I be responsible for the costs of an asylum seeker if I filed I-134 for him while he was applying for F-1 visa before?

I am a permanent resident (green card holder). I have a relative who is visiting as a tourist. He wants to start school and for that I want to be a co-sponsor for him as he applies to the school for F-1 visa. For that, I will also need to file I-134 Affidavit for Support. After that, if he decides to seek political asylum, he will become a public charge. In that case, would I be responsible for this costs due to the filed I-134 if he applies for public assistance programs?