I have ignored them.
This is not something you want to ignore. You can be sued. If an employer underpaid paid you, you would want them to make up the difference right? Same way the other way around. Them promising a bonus does not change the fact that your overpayment is an overpayment and not a bonus. Also you not having the money does not exempt you from having to pay, unless you enter a situation so impossible that you need to file for bankruptcy.
Let's assume your employer takes you to court. Judgments take a while to go away. Your state will likely give the judgment creditor a long amount of time to collect the debt. For example, California law allows ten years to collect. During that period of time the judgement may collect interest.
Now you have two options:
Ignore the problem and potentially face bad credit for 7 years, calls and letters for 10 all while getting charged interest. Depending on your state, your wages may be garnished or you could face a bank levy.
Tackle the problem head on. Call your previous employer and explain the situation. You may even be able to negotiate a payment plan over time.
Best of luck