Yes, it is possible for the party that defaulted to "reopen" the case. This can happen by filing a motion for new trial, an appeal or even a bill of review. I realize those terms probably don't mean much to you, but the point is - there are ways to "reopen" the case.
The iems mentioned above have different time constraints on when they must be filed. For example, a motion for new trial must be filed within 30 days after the judgment was signed. I cannot tell from your question whether you are the party that defaulted. If you are, then I advise you to immediately contact an attorney as the clock is ticking. Best of luck.
This answer is intended for informational and educational purposes only and should not be considered legal advice nor constituting an attorney-client relationship. This attorney is licensed in Texas.