I had Discover Credit Card in 1996 while I was in College, I was making steady payment until I wasn't working my part time job. To make a long story short, it's now 14 years later I received a letter of judgment to Garnish my paycheck from the "Marshal City of New York", when I called they told me it's a law firm that's suing me, when I called the law firm they told me it's the collection agency that Discover hired that's suing me. It's that legal or common practice

To answer the question in your subject, the answer is Yes. ANY debt remains valid until its paid.

However, there is a statute of limitations on how much time can pass before you can no longer be sued over the debt. And 14 years is WAY over that time.

However, its possible that they received a judgment against you within the SOL and are now enforcing it. Its unclear whether that's the case. If they are filing suit against you its too late. If they are using a prior judgment to garnish your wages, that may be legal.