Thankfully, your assets and credit are safe! From my perspective the "worst" thing that could happen, is that a process server may drop off paperwork, should your parents be sued at any point. No legal impact for you - just perhaps a little hassle.
Generally no, but that does not mean that the situation wouldn't be confusing to any creditors. Be sure that any property you own is clearly titled to you anything of value should be identified on your homeowners policy both to cover any damages and to insulate it from any recovery debt collectors seeking your parents assets
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