The shuttle stack broke up at ~73 seconds after launch of STS-51L. The Solid Rocket Boosters separated from the other elements and continued flying in a more or less stable manner (surprisingly). Air Force range safety personnel detonated the boosters at ~110 seconds after launch using the self-destruct system built into the boosters. (timeline reference)
I have not seen any writeups explaining the ~30 second delay to sending the destruct command. Range safety operated using preplanned procedures which included predicted impact of the vehicle on populated areas (see What rocket launch protocols (if any) are in place to prevent premature or late intentional self-destruct? for some details) It may be that the flight termination lines were not crossed until then, or possibly the procedures did not cover the case of two free-flying stable SRBs, requiring some human judgment.
Speculation on the time delay: This Google Maps image shows a shuttle launch trajectory - this is for an ISS flight, the 51-L trajectory would have been due east. Although the image is small, you can see that at 73 seconds the shuttle would have been well off the coast and traveling east at high speed (there were no significant trajectory anomalies prior to the stack breaking up). I doubt the limit lines were crossed in this case, and I would imagine the delay was due to human judgment upon having encountered a case never considered.
These pages from the 1982 Rockwell shuttle press manual show the SRB range safety system.
The debris landed in the ocean. Much of it was later retrieved including the critical segment which showed the burn-through from the O-ring, which greatly aided in the accident investigation. This is a photo of some of the debris on the recovery ship.(photo source)
The SLS SRBs do contain a flight termination system. Per this the first two SLS flights will use the same system as STS, after which it will be replaced by a more modern system.
...the Flexible Confined
Detonating Cord Assemblies (FCDCAs), which are currently used on the
SLS booster Flight Termination System that terminates thrust and
distributes booster propellant in the event of an anomaly. FCDCAs
will also replace the heritage shuttle devices on the Separation
System after the second SLS flight. FCDCAs are the industry standard
and serve the same purpose as the heritage CDFAs and CDFMs which were
unique to the Shuttle design. The new pyrotechnic devices are
lighter and more cost effective than the heritage shuttle devices.
Due to environmental exposure, the fuse encased in FCDCA can
develop fatigue cracks. EBA&D conducted risk-reduction testing, and
it was verified that no significant fatigue cracking was caused by
the SLS mission environments, and the FCDCAs would function properly
(Acronyms: Confined Detonating Fuse Manifolds
(CDFMs) and Confined Detonating Fuse Assemblies
(CDFAs)) EBA&D is a subcontractor.