[math-fun] Negative money

The proposed Reagan dime should have negative value (-$.10), just like his presidency. But this would cause massive confusion. If you give someone an RD, you might immediately owe them $.10. Therefore you have to keep your RD's carefully guarded, to avoid theft, which would cause you debt. But you want to get rid of all your RD's because they represent a debt. If you owe the IRS back taxes, they could send you a pile of RD's, but you could throw them away and deny getting them. What are the implications of having negative coins? I'm confused.