To answer
@Kira original question, it varies widely. No one can 100% tell you for sure what will happen, but I can tell you what is very likely and why it is people don't do this.
I am not an attorney, this is not legal advice, and I am speaking generally and out of personal knowledge not as an attorney.
So the bad news, they will just keep assesing fees, eventually they may (a lot do this a lot of the time) take you to court. It is likely they would win as you own deeded property and are legally responsible for the fees. If they win, they can seek legal fees. Again this is in general not just time share condos, etc.
Some good news, from the SC legal aid website. South Carolina law prohibits garnishment of unpaid earnings for certain consumer debts, and South Carolina Legal Services summarizes the rule broadly as: wages generally cannot be garnished for collection of a debt or judgment incurred in South Carolina, with exceptions such as government debts, taxes, and child/spousal support. I am not sure how real property works.
That being said, it is likely they can follow some sort of post-judgment enforcement process (these are often things like they send a letter to your bank from the court and freeze your funds, then get a "turn over" order).
Again there is a ton of nuisance here, it depends on your case, the law firm, the judge, and a million other things.
I would strongly STRONGLY suggest you have a free consultation with a local attorney before you stop paying and see what your exposure is, the above is not legal advice, but it is a very real possibility you might be exposed to legal liability.
Sources:
S.C. Consumer Code:
https://www.scstatehouse.gov/code/t37c005.php
S.C. Civil Remedies:
https://www.scstatehouse.gov/code/t15c039.php
S.C. Legal Aid on garnishment:
https://sclegal.org/brochures/wage-garnishment/
S.C. Post Judgement Law:
https://law.justia.com/codes/south-...1-frxkYDmOxpPlsbe5CdHgN36pOcPblNZ4YPusGtdEm1w