The TOC pays for the appeals process. However it is said that they pay the same fee regardless of the status (or success) of an appeal. I don't know whether or not that is true, although I would like to hope it is.
Regulation 11(3) of The Railways (Penalty Fares) Regulations 2018 would appear to suggest that the TOC who issued the Penalty Fare (or on whose behalf it was issued) is statute barred from instigating prosecution for an offence listed under Regulation 11(4) as soon as the appeals body has given its response to a first stage appeal, or upon the expiration of the 21 day period for the appeals body to give its response (i.e. if it doesn't response within the time period, the TOC is nevertheless statute barred from prosecuting).
The offences referred to under 11(4) are, in simple terms, a Railway Byelaws or RoRA offence.
So, if I am reading this correct (
@furlong ?), it would seem that, in your case, Chiltern are statute barred from prosecuting, assuming it has been more than 21 days since you submitted your appeal. Has it?
If this is the case, it makes a powerful argument for immediately paying any Penalty Fare you are charged, and then immediately appealing it. Even if the appeal is unsuccessful, and even if you have to sue the TOC (or process a card chargeback or similar) to recover a wrongly issued Penalty Fare, it would appear they are barred from prosecuting you.
Note that, however, this statute bar does not apply to anyone other than the TOC on whose behalf the Penalty Fare was issued. So if you are issued with a Penalty Fare by one TOC (say, Chiltern) on behalf of another TOC (say, West Midlands Trains), you would still be liable to prosecution by anyone other than WMT, and I would imagine Chiltern for example might well choose to proceed to prosecution if you tried to further appeal against a Penalty Fare, or tried to chargeback it.
An interesting development!