I took a phone jack off the wall and snipped the cable. I'm not getting any voltage between green and red, either AC or DC. I don't want to just leave a wire in the wall that could become live. How do I safely terminate this wire, preferably without tracing it all the way through the muddy crawlspace to its source?
They make tiny gray and blue wire nuts that ought to work, you could strip and twist all four wires together, trim, and twist on a wire nut. You could cap each wire individually, but I'd splice / short them all together.
I have heard two different schools of thought about "safing off" unused wires, especially wires you want taken out of use. With line voltage, some say it's better to short / splice them and / or bond them to the EGC, others say cap them separately.
I'll leave that discussion for another question, for a phone cable, it doesn't matter much. One wire nut on four conductors will hold more securely and less to look at.
If you can identify it, you should disconnect and cap it at the other end as well - probably in your house's telephone NID (network interface device).
If you want to be really thorough, tag it in the NID with a label where the other end is, just in case someone needs it in the future.