Why can't a person sell himself into slavery?

People often decry indentured servitude, whereby people paid for their travel to America with several years of service. But this seems like a perfectly sound trade given certain assumptions about the terms of that service, e.g. you can't starve or abuse the servant. Is that right? If so, why can't a person sell himself into slavery? For instance, suppose that my family is poor, so I arrange with someone to give my family money in exchange for me becoming their slave, i.e. literally becoming their property. Is that possible? Should the law forbid that?