Let’s suppose a suspect is arraigned and his family puts up a sizable amount of bail to release him from jail.
Let’s also suppose during the time between his release and his court date the family becomes financially burdened.
Can the suspect (with a sense of concience and honor) request that he be placed back into jail so the family gets back the bail money?
I don’t know about that exact scenario but, if the bail is truly large, the family most likely gave 10% of the bail to a bail bondsman and the bondman paid the rest of the bail. In that case, nobody is getting anything back. The bail bondsman keeps the 10% and gets the rest back when the accused shows up for trial.
I don’t know what can be worked out if the family can actually put the whole say, $100,00 up themselves.
In addition to what Shagnasty said, if the person out on bail is arrested for another crime moments after being bailed out, the bail bondsman isn’t going to refund anything. This also applies if a judge decides to revoke one’s bail for any reason.
I’ve never seen a family ask for bail money back if they did put up the whole amount, those I suppose they could. It’s going to cause some awkward feelings at the next family reunion if they do. 
If you have ever watched Dog The Bounty Hunter there are quite a few bail revocations. In the shows I saw, the people got whatever they put up (minus 10%) back.