There is no single answer and it depends on what the nature of the lithosphere of the "following" plate is and/or the geometry of the boundaries between the subducting plate and the "following" plate. Some options are:

1. Plate that follows has oceanic lithosphere with a mid-ocean ridge between the subducting and following plate and subduction ceases before the ridge reaches the subduction zone. Effectively the idea is that subduction is driven by the negative buoyancy of the subducted slab, which is a function of the age/temperature of the slab. The piece of lithosphere adjacent to an active ridge is pretty warm, young, and positively buoyant so it will resist subducting. Depending on the relative competition of forces what may happen is that subduction slows down as this young lithosphere approaches the ridge (resisting subduction) and then the slab rips off (i.e., it detaches) because the slab pull force overcomes the strength of the slab nearer the surface. This can effectively terminate subduction (no slab pull = no subduction). As to what happens from there, it will depend on the specific forces, but most likely the ridge might die and there will be a general reorganization. That reorganization might see a wholly different set of plate boundary kinematics or the subduction zone might "jump", keeping effectively similar broad scale kinematics but with the subduction zone in a different place. It might also jump and reverse polarity. Or it might transition into a new type of boundary depending on the kinematics of the plates that meet. This option is quite common if the ridge is roughly parallel to the subduction zone (e.g., Burkett & Billen, 2009). Semi-parallel ridge subduction does happen though, and for it to happen, usually some amount of complicated geometries and "3D effects" are required (e.g., Burkett & Billen, 2010).
2. Plate that follows has oceanic lithosphere with a mid-ocean ridge between the subducting and following plate and subduction ceases after the ridge subducts. A geodynamically unlikely option, but assuming the ridge is roughly parallel to the subduction zone, this would also lead to slab detachment and cessation of subduction and reorganization depending on the kinematics of the two plates that now meet.
3. Plate that follows has oceanic lithosphere with a mid-ocean ridge between the subducting and following plate and subduction continues after the ridge subducts. This is relatively common if the ridge is very oblique or orthogonal to the subduction zone. In this scenario, the ridge will subduct and in many cases a "slab window" will open along the subducted segment of the ridge. You can picture the ridge effectively unzippering down the length of the subduction zone, kind of like this. This makes some specific predictions about what you would see in the upper plate, specifically a gap in normal arc volcanism and instead magmatism that is more indicative of direct mantle interaction with the upper plate rocks.
4. Plate that follows has continental lithosphere. This would largely require a plate with subduction zones "across" from each other and at the moment that the two subduction zones meet, the result will depend on the nature of the adjacent section of the other overriding plate (is it continental or oceanic) and the relative motion between the two plates that meet. If the other overriding plate is oceanic and the kinematics favor it, subduction might continue via a polarity flip where the formerly overriding plate becomes the subducting plate. Instead, subduction might cease and the boundary might change kinematics (e.g., become a transform boundary).