It would have been in GM's interest to keep Studebaker alive, remember that they pulled out of racing in late '63 because even good publicity might hurt them in the investigation of their "monopoly" by government officials.
They did give Leo Newman and Nate Altman good deals on Chevy V8s and other components of the Avanti II for the same reason, "See, anybody can be in the car business!"
The problem was the Studebaker-Packard board, made up of accountants, not car people. When the recession of '58 cut everyone's car sales, they saw cars as a poor return on investment. Engineer/President Harold Churchill kept them at bay for a while with his ingenious adaptation of the full size Stude body with a shorter hood and trunk to create one of the first "new compacts", the Lark.
By 1962, sales were down again in the face of compacts from Chevy, Ford, Mercury, Buick, Olds, Pontiac, Dodge and Plymouth, to say nothing of the compact pioneer American Motors.
Studebaker's dynamic new president Sherwood Egbert made bold moves like the Avanti, the updated GT Hawk, availability of superchargers, disc brakes and a sliding roof station wagon. Andy Granatelli came aboard, setting records at Bonneville with stock and modified '64 Studes. The Studebaker prototypes for '66 and '67 were as ahead of their time as the Packard Predictor dream car was in the mid-'50s. I believe you can see them at the Brooks Stevens auto museum.
At a critical "success is just around the corner" point, Egbert was sidelined with lung cancer, unable to fight back against a board that wanted to stop making cars. Canada wanted a domestic automaker, and lightly-restyled Studebaker cars were made there through '66, once again with Chevy sixes and eights.
Studebaker Corporation continued on for many successful decades, making many products (including STP, I believe), but no more automobiles.