The California Streets and Highways Code generally but not always requires, in the law authorizing a mid-route relinquishment, that the relevant local government maintain continuation signage for the relinquished segment to guide motorists to the rest of the route. This requirement is often ignored.
How I've been handling it for the usaca preview system:
(a) if the relinquishment is at the end of a route, treat it like a truncation;
(b) if such signage is known to exist, and is required by state law, we've left the route intact, as with relinquished CA 1 segments in Dana Point and Santa Monica;
(c) if there is no such signage (even though required by law), but the route can be easily followed without the signage, we've left the route intact. Relinquished CA 1 through Newport Beach is one where we've left the route intact despite lack of signage, since it's just a straight line through the city. Relinquished CA 79 through San Jacinto, and CA 160 in Sacramento south of the American River, are impossible for motorists to follow, due to several unsigned turns (plus there's an End CA 160 sign at the southern city limits), so I removed those segments.
These rules are open for discussion, before usaca goes active.
I guess for South Dakota, the key issue is whether signage for the relinquished segments is required by law, rather than just left behind by South Dakota DOT but with no obligation by the Sioux Falls city government to maintain the signage.
