In other words...not too different from when the broadcast signals went from analog to digital, & you could no longer use an old VCR with analog-only channel capability to record programs.
Barring finding a new VCR recorder that has a built-in, cable-compatible digital tuner, your best bet to be able to record 1 program & watch a 2nd program simultaneously is this:
-- Connect the wall jack line to a 2-way splitter
-- Run the line from each output of the splitter to a separate digital adapter (#1 & #2)
-- Connect #1 directly to the TV set
-- Connect #2 to the VCR, then connect the VCR to the TV set
Your VCR will be able to time-program as normal (as long as you set it to Channel 3/4), you'll just have to make sure digital adapter #2 is set to the correct channel beforehand. Biggest issues, apart from the extra cost, are remembering to set the channel before going to bed/watching another program, switching channels to catch consecutive programs that are on different channels, & dealing with only being able to record 1 channel at a time while at work/out to dinner/on vacation/etc.