undetected plumbing leaks
Leaks that go undetected for any amount of time can cause hundreds, or even thousands, of dollars in damage. This tub has been leaking for quite some time to have caused so much damage to the subfloor and supporting joists.
rusted cast iron tub
The cast iron tub has rusted around the drain. This has made the area porous and subject to leaking. This house was built in 1947, so you expect to find some issues once you start exploring the crawlspace.
confirm the moisture content
I could see the water dripping from the pipe, but you still need to use a moisture meter to confirm the moisture content in the surrounding area.
This could have been discovered long before it caused such extensive damage. If you have a crawlspace you should inspect it annually to prevent small problems from becoming HUGE problems.