Once an HOA Lien is placed on a property, whether the lien be valid or extinguished in a foreclosure,
Whose responsibility would it be to release the HOA Lien?

If there is a lien on the home, it does not matter if it is valid or not as long as it is actually there, it is considered valid until proven invalid.

In a foreclosure, the first mortgage is paid first from the money in the sale, if there is any money left, it goes to a second mortgage, and if there is money still left, it would pay any other liens.

So when they don't get paid from the foreclosure sale, they can sue you and get a judgement and come after the money from your personally, dependent upon terms of the HOA agreement, and state laws.