‘I have a home on my parent’s land in New Mexico. I found out they have a property tax lien for unpaid taxes. Can I lose my home?’
Yes. If the lien is against this property, it could absolutely be foreclosed. You might get some money in the foreclosure, but you almost certainly wouldn’t be able to keep living there.
If it’s at all possible, your safest bet is to get the taxes paid. If your parents can’t or won’t do it, do it yourself.