The RFA tender system is generally bad for the players and good for the RFA's team. It mostly applies to undrafted free agents who actually perform well enough to be valuable to their teams. Teams can tender a RFA and 1st round, 2nd round or original round level. The tenders require the team to offer the player a 1 year non-guaranteed contract with compensation depending on tender level; compensation is artificially low. The contract also has ZERO guaranteed money, so the player can be cut at any time. Little job security. Other teams have a window to try and sign the player by offering him a new contract. The tendering team has 5 days to match the offer. If the tendering team does not match, the other team can sign the player but must give the tendering team draft pick compensation. At 1st and 2nd round level, that's the draft pick that must be surrendered by another team that wants to sign the player. It the original round level, the round of the pick that must be surrendered is equal to the round the tendered player was originally drafted in. Since RFA's are almost always undrafted, the offering team is not required to give up a draft pick to sign the RFA.
In the real world, other teams rarely succeed in signing away RFA's tendered at the 1st or 2nd round level. They don't want to give up the draft pick. Many teams don't even bother making offers to tendered RFA's because they know the tendering team will match their offer.
The worst part is what happens to some tendered RFA's after the window where other teams can make offers and sign them ends. Per overthecap.com:
"Often once the RFA free agency period is complete teams will use the leverage to reduce the costs of these contracts, specifically for the low tendered players, since they know the players’ options are limited. What they will do is offer the player a minimum salary and a guaranteed bonus somewhere between $100,000 and $300,000. The total compensation is lower but at least there is some job security."
For some RFA's that means trading a crappy original round tender contract ($1.6M) for a multi-year low dollar crappy contract with some guaranteed money/signing bonus.
Cunningham was tendered at the "original round" level. Patriots had some interest but declined to offer him a contract since they knew the Rams would match their offer. Cunningham has more value to the Rams than the Pats since he figures to be the Rams' primary #2 RB/3rd down back. Rams had plenty of cap space needed to match and sign as well.
Like most NFL players (and all fringe ones) Cunningham is going to want a bit of job security/guaranteed money. Will Cunningham cut a deal (multiyear?) with the Rams for substantially less than $1.6M in exchange for a little guaranteed money? The Rams leverage to get Cunningham to take less $ is their ability to (i) bring someone else in to replace him if an opportunity presents itself, or (ii) cut him in training camp after teams have spent their free agent money. At that point Cunningham would be looking at league minimum offers from other teams with zero signing bonus.
Compare Cunningham's situation to Brian Quick's. Fortunately for Quick, he was not a RFA. Rans gave him basically a $1.75M guaranteed 1 year contract. Fair?
