The postulate put forth by others on this board stands as accurate.
If WKJY was running HD, and WHLI was on the HD2, then WKJY HD2 could run WHLI's format 24 hours. WHLI at 1100 AM would still be required to go off the air after local sunset.
Heres another interesting point. There has been somewhat of a push to allow low power FM Translator stations to carry programming from AM stations. Here's the interesting part. If an FM translator station was carrying programming from WHLI, or any other daytimer, the FM translator could stay on the air and carry would-be programming from the station 24-hours a day, irregardless of the fact that the main AM station would still have to sign off at sunset. I believe the issue of FM translators being able to carry AM programming is still open and unresolved with the FCC.
Back on track though, WHLI could still maintain a 24 hour broadcast schedule if they wanted to. Its just kind of pointless though because with the transmitter off, nobodys going to hear it. If however there is an alternative means of distributing the programming, such as an HD2, an internet stream, or an FM simulcast, then WHLI could very program for 24 hours. The actual radio signal of WHLI 1100 AM would still remain aq daytime only signal.
On a semi related note, I sometimes wonder why WALK FM doesn't run WALK AM 1370 on either their HD2 or HD3. As far as Barnstable, if they should install HD at their stations, they could do all kinds of simulcasting. For instance they could carry K-Joy on WLVG HD2. They could put WRCN on WMJC's HD2, and WMJC on WRCN's HD2. ETC.