Microsoft bought SoftImage, as a part of the effort to displace high-end Unix workstations with PC's running NT. It was all over, but the shouting. Alias transformed Wavefront into Maya in roughly this timeframe, while MS starved out "dot release" life support on SoftImage...
I wrote Falling Bodies, the ragdoll physics plug-in for Softimage, back in 1996-1997, so I got to see this happen. Back then, Softimage was #1 in Hollywood. Microsoft bought them, and when I went up to Redmond, the Microsoft guys were talking about making Softimage mass-market software. But that never happened. It was too hard to use, and required more graphics hardware than most users had back then. (I had a $2000 Dynamic Graphics card in an NT workstation back then. Every low-end GPU today has far more power.)
So Microsoft sold Softimage to Avid. Avid made overpriced film and video editing systems, sold with semi-customer hardware and built into cool-looking furniture. Softimage had a good video editor in addition to the 3D line, and that's what Avid really wanted. They had no clue what to do with the 3D product. They did convert from Softimage to "Softimage XSI", which broke all existing plug-ins and didn't have a plug-in API that worked. That's when I dropped Softimage.
As video editing went mainstream and Avid's sales of overpriced furniture declined, Avid sold off the 3D product to Autodesk. Autodesk had sort of become the default acquirer of 3D animation products. Most of them came from small companies with tiny product lines. Maya came from the merger of Alias and Wavefront and the mess at SGI. Autodesk picked up Lightwave and some other stuff, and of course they already had lots of 3D engineering tools.
This worked out well at Autodesk. The architectural design programs were integrated with the good renderers from the animation world, and images of what new buildings were going to look like got really good. (Adding a radioisity renderer with very realistic lighting models allowed architects to get all the right light fixtures in the right places.) Autodesk's real business is tools for making real physical stuff (their internal slogan is "If God didn't design it, one of our customers did"), but there's a lot of crossover between 3D design of real-world stuff and 3D design of animated stuff.
Softimage has pretty much been a has-been product for years now. After 20 years, it's probably time to phase it out.