Behaviour of a (broken?) transformer
Many of these transformers have an internal fuse on the primary winding. The terminals for these are sometimes visible on the winding terminals. These are usually designed to offer both over-current and over-temperature protection.

I have no explanation for the loss of the C, centre-tap, continuity on the secondary. It may also have a fuse but it would be a surprise that both failed at the same time.







simulate this circuit &ndash; Schematic created using CircuitLab

Figure 1. Possible internal arrangement.