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?
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1$\begingroup$ There were no crew procedures for loss of SRB thrust. nasa.gov/centers/johnson/pdf/359893main_AESP_G_O_4_P%26I.pdf Before liftoff, the SRBs were not ignited. $\endgroup$– Organic MarbleFeb 10, 2022 at 15:06
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1$\begingroup$ @GdD that question is about failure to separate, not loss of thrust. $\endgroup$– Organic MarbleFeb 10, 2022 at 15:22
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3$\begingroup$ How does a solid motor cut out? What are the flight regimes that make you certain they would cut out? $\endgroup$– BrendanLuke15Feb 10, 2022 at 15:26
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3$\begingroup$ The only way for an SRB to flame out is by depressurization. Shuttle SRB in particular can not be depressurized in a controlled manner. So the only scenario where SRB could flame out would be the "Challenger disaster", i.e you have much more to worry about than losing thrust or balance. $\endgroup$– user3528438Feb 10, 2022 at 15:27
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3$\begingroup$ They don't @BrendanLuke15, once lit a SRB burns until the fuel runs out, or explodes, that's about the only 2 options. $\endgroup$– GdDFeb 10, 2022 at 15:28
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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.
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$\begingroup$ @AntonHengst yes, they had range safety packages installed. So they could in fact be "stopped". $\endgroup$ Feb 10, 2022 at 21:39
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1$\begingroup$ @TooTea consider yourself promoted to the rank of "Captain Obvious" :) In all the times this stuff comes up, I have consistently said that there was nothing that could be done. $\endgroup$ Feb 11, 2022 at 19:25
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1$\begingroup$ @OrganicMarble Oh, I only meant to (half-jokingly) point out that this manner of stopping thrust is not going to be useful for anything else than blowing everything up, exactly because I have seen many questions like "why didn't they do X to save Challenger". Sorry if that came across the wrong way. I guess I should delete my comment. $\endgroup$– TooTeaFeb 11, 2022 at 19:32
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1$\begingroup$ @DekoRevinio Sorry, but that makes little to no sense. The solid propellant is a mix of fuel and oxidizer, it does not use oxygen from the atmosphere (that's kinda the definition of a rocket engine and what makes it work in space). Once you set the mixture on fire, it will keep burning until it consumes itself and trying to seal it in a container is just going to make it go boom. $\endgroup$– TooTeaSep 21, 2022 at 6:59