I don't think they block, but there will be lots of
re-direction. If the incident happens to be at AMK or Jurong, then
it's all right, as both stations have a middle platform. Trains
could be easily deployed to help out.
But if it's at other stations, all passengers will have to alight
and wait for the next train. They do this alternatively (alternate
could be wrong, I never stayed long enough to observe, don't want
to pay $2 
) until
the train services resumed back to normal. There will usually be
buses to serve the passengers if a long delay is expected.
This will make sure that services are as normal as possible, with
some delay in between.
