It happens quite a bit in PA. Cubs are born in PA in Jan or Feb while the sow is in hibernation. Our bear season comes in the end of November and in over populated areas it comes back in in Dec during deer season. The cub that are running with sows are well able to take care of themselves since they are around 9 months old when the season opens. It used to be illegal to kill a cub in PA, however it got a bit ridiculous at the check stations congratulating a hunter with a bear over a year old normally a sow and the next guy in line has a 110 lb male that is under a year old, cub get a citation and loses his bear. I have weighed cubs over 125 lbs and adult bear at under 100 lbs. When the law changed, most people still tried to leave cubs run, however, since many hunters have never seen a bear in the wild, unless the cubs are close to the mother where a size comparison can be made they will shoot the first one they see unless they are experienced. Then when they walk up to the bear they find ground shrinkage, a cub. allowing cubs to be taken certainly did not hurt our bear population, our harvests remain between 4,000 and change and 3,000 and change. If the OP's seasons and birth times are abut the same as ours, cubs are able to take care of themselves if the sow gets shot, that doesn't mean you have to shoot it but the cubs will be OK.