What you see in the picture is the Magnetic Amplifier coil. According to the schematic I saw, the SP-200 brings in single phase to the primary of the power transformer, one leg goes to a pair of diodes, the other passes through two phased legs of a magnetic amplifier (figure-8) where swamping current apparently charges the center coil of the three, saturating the two outer sides where the large, flat mag-amp coils pass.
The part that I find peculiar, is that one leg of the mag-amp looks like it was physically welded ON... like something metal fell in there, and shorted it to secondary's return, and I can't tell for certain from the resolution of the snapshot, but it looks like it was bouncing around in a couple spots.
IF this mag-amp failure occurred as a result of a bad connection, the hot-spot would be from that location, and percolate gradually out. If the mag-amp fractured, it would do same, and open up from that point until failure. Without seeing closer, it's hard for me to figure how this happened, but it isn't pretty, and fixing that winding will be an interesting challenge.
Because of how the mag-amp is damaged, the success of trying to recover the rest of this machine relies on finding some replacement for that mag-amp winding... either that, or bypassing that side, and figuring that he'll only have partial range control...
But I can understand why OP would be miffed about the deal. I wouldn't jump to a conclusion that someone sold it with knowledge and intent, because I've seen plenty of things like this happen without such. Things happen over time, things in shipment. I've gotten so that my S.O.P. for anything that comes to me, gets opened up for an internal inspection prior to a smoke test... I guess I prefer to have the covers off, so that the smoke has an unimpeded exit path... and while that's said in humor, there's inherent truth in that I've seen smoke, and with the cover off, I saw it's source and path quick enough to knock the power off and move in for a really close look, to get a quick resolution.
With regard to JST's note on capacitors, it has been my experience in welders, radio transmitters, and railway traction inverters that capacitors are most heavily stressed and rapidly degraded by voltages in excess of their working ratings, and while a DC component, or a low-frequency AC component would pass, there are many opportunities for very high frequencies to develop, or find their way into circuit areas where such are neither intended, or expected by the designers. Anything that intendionally develops an arc, either AC or DC, is subject to creating a cornucopia of wideband high-frequency noise, and it's like mice- all the protective circuitry in the world will NOT stop it from finding ways into places we really don't want it... and the weakest points will advertise themselves in many ways. I've grown old enough to expect the unexpected, which I guess means I probably just expect everything, and assume basically nothing. I DO know, that when my designs incorporate belt-and-suspenders for things I didn't expect, I had no failures, and I've also come to the conclusion that if a part failed, up-rating the part's limits was always the proper course of action.
But as for this SP-200, I've never made, or attempted to repair a mag-amp. Men built it, so it can be done, but I haven't done that YET... I hope a solution can be found for it.