Not automatically. Bail is determined at a specific time and can change with circumstances, but if you were bailed out at $10,000 because of a felony charge, then that was what was appropriate at the time. It is possible to reduce bail once you've been released, but the first question you need to ask is whether it will make a difference. If you went through a bail bondsman, then the bondsman is not going to refund any money, so what's the point in attempting a bail reduction? Attempting a bail reduction after you've posted bail will most likely be unsuccessful since the courts will figure what's the harm when you're already out of custody. Now, if you're still in custody when your charges get dropped/reduced, then applying for a bail reduction is both appropriate and more likely to succeed (depending on the circumstances).
I both agree with attorney Thiagarajah's answer and disagree on an important part.
Assuming the case is still pending, you can ask that your bail be dropped and you continue to be released on O.R. - I do these often with success. The key is to have your attorney emphasize that you've not missed any court appearances (or they haven't on your behalf) and obviously are not a flight risk.
Good luck with your situation.
If your friend posted a cash bail with the court, then your attorney absolutely should ask for a release on your own recognizance (an "O.R." release). That way, your family member can get their entire amount of bail back.
If you went through a bail bonds company, then the fee is what it is and the bail company's fee is what it is and has already been paid. You can always ask, if your bail is reduced, if the bail company would consider cutting you a break and refunding part of the fee, since they're getting their money back without further risk. The worst they could say is no.