This sounds like aggression, or fin rot. What's your stocking, and what specific fish are being effected maybe you have an aggresive fish
Fin Rot Information
Symptoms
-Ripped tails, bloodshot, black edged, or has a fuzzy white appearance on the edges of fins
-The fish will become unusually inactive
-Won't eat
-chunks out of tail missing
-Looks pale, and looses lots of color
Causes
This profilic disease is caused by stressful water conditions primarily but here are a few main examples of the conditions it is most likely found in
-Poor water quality with unacceptable amounts of ammonia, along with nitrites and nitrates
-Nippy tankmates
-Incompatible tankmates
-Tailbiting
-Plastic plants ripping fins constantly
-Over feeding
-Over crowding
-Sometimes after a disease, while the bettas immune system is low it can strike unexpectedly
Treatment
This disease is most commonly treated with mainly
-daily water changes of around 25-50 so more diseases dont settle in while the Betta is vulnerable
-a high quality fin rot treatment. Use tetracycline or Ampicillin for the best possible results
Prevention
-Keep the water clean
-don't over feed
-choose the right tankmates
-make sure that the bettas fins are always in the best shape
-keep the water heated
-change the water weekly