There was actually a procedure in the days of 101s holding down all the local services to Falkirk Grahamston, Stirling, etc. If an inbound train had one engine out, this was advised forward, a loco was sent down from Eastfield to Queen Street, the dmu was called on into the same platform, and the loco banked the unit back up to the depot. And another dmu was sent down to an adjacent platform to continue the diagram.
My only 101 departure ever from Queen Street was a substitute for the 2 x 27 push-pull to Edinburgh. Only three cars, and with standees. It was probably doing 20-25 mph by the top.