Do male bears stay in area of female with cubs???

Adult black bears generally will go their separate ways. If a food source is good, you'll often see multiple bears concentrating there. Sows with cubs, small sows and boars, big boars. I have observed on many occasions where a sow with cubs was feeding, a larger male approached, and the sow took the kiddos and left. Larger boars are territorial over their food, and generally will try to run off other bears when he encounters them in his food. Back in small game season, I videotaped seven minutes worth of footage of a big sow and a mature boar feeding in a field. A larger boar was in the field, and was trying to run off the smaller one. He harrassed the daylights out of the smaller boar. They were in a sorghum and pea field. The bigger boar would approach the smaller one. They'd square off, stand up and fight. Then the younger boar would try to feed again as the bigger boar circled around, and approached him again. This process was ongoing already when I approached the field, and it continued after I left. They were bringing the fight in my direction. I could hear them growling while fighting and I could see their teeth. At that point I figured it best not to be caught in-between two bears actively fighting, so I left.
It was the food they were fighting over. Generally, you won't see that many mature bears together. Not in the fall, at least.