The hot material of the dome that moves downslope will produce a pyroclastic flow, specifically what is known as a “block & ash flow“. Here is a brief video of one from the dome collapse at Soufriere Hills, Montserrat.
This hot pyroclastic flow (or nuee ardente) will melt snow/ice on Redoubt and mix with runoff to form lahars that will travel down the drainages on the edifice, possibly all the way out to the inlet.
Generation of pyroclastic flows from dome collapse. Figure courtesy of the USGS.
Impressive, eh? Of course, it might not happen exactly like this. There are many variable (extent of collapse, pressure from underlying magma, magnitude of pyroclastic flows generated and many others), but more than likely, block & ash flows and lahars will be generated when the dome does collapse.
The latest from AVO suggests they think it will happen soon and without much warning, so keep an eye on the webcams (DFR and Hut).