You have no idea what you're talking about. There is no limit on the number of players that can be offered. There are limits on the number of total scholarship players on any team, the number of preferred walk-ons, and how many kids you can have in pre-season fall camp. There is also theoretically a limit on how many players you can sign in each class, although there are a number of ways around that.
Every team in America offers dozens of more players than they have room for, typically on some sort of first come, first served basis. For example, a few years back, Iowa had one ride available for a RB. They had offers out to DeAndre Johnson, who had torn his ACL earlier in the season, and current Wisconsin stud James White. Johnson committed to Iowa first, so the coaches told White they didn't have enough room and couldn't take him. Something similar happened last year on a kid out of New Jersey. He had been going back and forth with the coaches for the better part of a year, then like the day before signing day he tries to commit and we tell him we don't have any room left. His high school coach was p*ssed and it became a minor issue in the media.
Oversigning is completely different. That's when you knowingly sign more kids to scholarship offers than you have spots available, with the idea being that you are either going to chase some underperforming kids out of the program (forced transfers, phony medical hardships, etc), or else you have the situation that occurred at I believe Texas Tech a few years back when 2 or 3 kids showed up for fall practice expecting that they had full scholarships, only to be told by the coaching staff that they were over the limit and seding them off to some JUCO.
This practice is technically not illegal by NCAA rules, but I believe the Big Ten has specific rules forbidding it. The league still allows each team to sign 3-5 kids over the 85 scholly limit, as long as they document how they plan to get down to 85 by the start of fall camp. Most teams have a few academic casualties, transfers, etc. that will allow them to account for the extra numbers.