Typically, the CC company itself won't follow the customer very far upon a default (though it certainly can act as its own debt collector, or hire an agency for a fee to do the collection). What most often happens:
- CC company pesters you for a few months.
- CC company sells debt to a debt collection agency.
- Debt collection agency pesters you for a while, typically offering a settlement at a reduced rate (which is still greater than they paid the CC company for the loan).
- Eventually, the debt collection agency sues you for the amount of the loan.
Once they do that, assuming they win the lawsuit, they can do the following:
- Seize the amount from bank accounts by court order (if that amount exists)
- Seize property you own (other than your primary residence, furniture, and other protected items)
- Garnish your wages (if they are not protected from garnishment - for example, SSD income is protected)
- Put a lien on your non-seizable property (such as your primary residence) so if you sell it, they take their cut from the proceeds
They cannot "force" you into bankruptcy, but they might make it so you have no better options (if bankruptcy is less painful than the above, which it often is).
They certainly can (and will) report to the credit bureaus, of course.
For more information, Nolo has a decent help site on this subject.
Different jurisdictions have slightly different rules, so look up yours. Here is an example (this is from Massachusetts).
Not every debt is sued for, of course; particularly, pay attention to the statute of limitations in your state. (In mine, it's seven years, for example.) And it's probably worth contacting someone locally (a legitimate non-profit debt relief agency, or your state's help agency if they have one) to find local rules and regulations.