Our house was foreclosed by a roofer who put a lien on our homestead in Texas. The roofer bid $3000 against his $80000 lien. He has not done anything else. He has not paid off the first lien, a mortgage. If a second lien holder forecloses, what responsibility does he have to the first lien holder?
No. The roofer cannot be compelled by you to pay off the first lien.
The foreclosure of the roofer's mechanic's lien is very likely an event of default under the first lien, but the decision of the first lien holder to foreclose as a result of that default is up to the lender on the first lien and not you or the roofer.
The roofer can have you evicted (ignoring COVID-19 based eviction bans, if any), without paying off the first lien and is free to let the first lien go into default too, although doing so would cause the roofer's post-foreclosure ownership interest to be wiped out if the roofer does not pay it off once the first lien is foreclosed upon.
Realistically, the roofer will probably hire a realtor to sell the house subject to the lien and seek to pay off the first lien in connection with that sale, or will refinance the first lien (possibly by a mere loan modification with the existing lender).