I'm certain there are several flight regimes where this could happen, and that the procedures should be different for each one. For instance, this is a very different question before lift off than it is at 40km. So, presuming that the SRBs were burning and then both cut out, what was the procedure at each regime, and what would have happened?
If they fail to ignite for any reason, then great success if both and not just one: SSMEs can then be shut down and the Shuttle stays on the launch pad with the flight over. SSMEs are started before the boosters are ignited. There is some machinery involved in the booster ignition, so it cannot be said this absolutely cannot fail.
Once started, the Shuttle booster cannot be stopped even deliberately.