The answer is “the state is now a bank” and as it controls the price floor and the amount in circulation it can control the market price.
The price is whatever the state wants it to be.
If tokenized, the benefits would definitely be traded in the open (although perhaps black) market. There’s already a black market for food stamps
A state sponsored welfare system based on a proof of stake protocol would actually be a profit center for a state government if the token was permitted to be traded on the open market with the state acting as an underwriter.
— Bryce H.C. Weiner (@BryceWeiner) August 28, 2019