alt Hacker NewsSSD offload is always a possibility with good software support. Of course you might easily object that the model would not be "running" then, more like crawling. Still you'd be able to execute it locally and get it to respond after some time.
Meanwhile we're even seeing emerging 'engram' and 'inner-layer embedding parameters' techniques where the possibility of SSD offload is planned for in advance when developing the architecture.
For conversational purposes that may be too slow, but as a coding assistant this should work, especially if many tasks are batched, so that they may progress simultaneously through a single pass over the SSD data.