From:
2020 NIT selection show: Time, TV channel, date | NCAA.com
2020 NIT: Teams, how it works
Regular-season conference champions that don't make the NCAA tournament automatically qualify for the NIT.
Also, the teams listed by the NCAA Men's Basketball Committee as the "first four out" for the NCAA tournament earn the top seeds in the NIT field. Last season, UNC Greensboro, TCU, Alabama and Indiana received No. 1 seeds for the NIT.
Reportedly NCAA decreed several years ago a team with a losing record cannot go to the NIT, but I cannot confirm that to be the rule. If SU or any team has a losing record they should be banned from participating.
Obviously, given the above SU is not likely to be an NIT top seed. In fact, one projection has SU being a 5 seed --- in the NIT.
Oh, for the good ol' days