For the sidestep, see Anchorage (PANC) ILS or LOC DME Rwy 7R.
Now, assume Approach or Tower asks you as above, "Can you accept 13L," as you are inbound on the VOR/LOC/ILS?NDB 13R approach. You are currently IMC. How can you accept the change in runway if you cannot see it? How do you know you will be in a position to make a normal approach and landing on 13L after you break out? In that case, the ONLY way to land on 13L is to continue on the 13R approach until you break out, and then and circle to land on 13L IF AND ONLY IF you break out above circling minimums. If there are no circling minimums published for that 13R approach, you CANNOT land on 13L from that approach because it is NOT AUTHORIZED! If you have to go around FOR ANY REASON, you are obligated to follow the missed approach procedures for the 13R approach unless instructed otherwise by ATC. PERIOD!
OTOH, if you are VMC when offered the change of runway, and you accept, you SHOULD be cleared for a visual approach to 13L. You abandon the VOR/LOC/ILS/NDB approach to 13R in favor of a visual approach to 13L.
I believe anything other than a clearance for a "visual approach" or "circle to land" (or "sidestep" where appropriate) is a mistake in ATC clearance. If you receive only the "Cleared to land" as above, you should respond with something like, "Understand cleared visual approach (or circle to land) and cleared to land 13 LEFT." If ATC has something else in mind, it is now their responsibility to correct your misunderstanding.