A few things could be going on here....
First step is to seperate the beardies immediately. Beardies should never be housed together anyway, and they defiantely should be alone if any health problem is noted.
Its possible a bacterial infection is in the feet and is causing gangrene, this would need to be treated with antibiotics and possible amputation. Gangrene is very dangerous as it will continue to spread until it kills the dragon if its not treated.
Its also very likely that the dragons have been fighting and you have not noticed. Often times the first sign of aggresion in beardies is nipped toes and tail tips.
How old are you dragons?
Do you know the sexes?
Is one much bigger than the other?
What size tank are they in?
What is the substrate and how often is it cleaned?
Answers to these questions may help us figure out whats going on.
Seperate the beardies, put the one with the wounded feet in a tank on paper towels with good basking temps and cooling temps and access to good uvb light. You can soak the feet 2-3 times daily in a diluted betadine or chlorhexidine solution and apply triple antibiotic ointment to any open sores. This MAY help to temporarily slow infection.
Continue offering the wounded beardie food, it is very important and a very good sign if he eats.
Its really important that you get to a vet. If there isn't one near you then its worth the long drive. Often times people have to drive 2-3 or even 4 hours to find a good herp vet. But unfortunately there are not a lot of exoitic specialist vets and traveling to find one is just part of the responsiblity of owning a reptile. Make an appointment for as soon as you can. The vet will probably want to prescribe antibiotics and may want to amputate the feet. Beardies can easily live full and happy lives with missing feet, i have seen it tons of times.
Dont delay in getting your beardie to a vet.
good luck
-----
0.1 Bearded dragon (Hannabil)
0.1 mexican Black kingsnake (Morticia)
1.1.2 Leopard Gecko's (Pogo, Louise, Orion, Jeffrey Nothing)
0.0.1 Tokay Gecko
1.0 Blue Tongue Skink
0.0.1 Reverse Okeetee Corn (Autumn)
0.1 Bullmastiff (Asha)
4.1 Cats (Poe, Tucker, Abhid, Felicity, Emmy)