Standard carriers underwrite to a narrow loss profile, and a serious violation falls outside it. The usual mechanism is non-renewal at the policy anniversary rather than a mid-term cancellation, which gives you some runway to replace it.
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A non-renewal is not a judgment about you personally; it is a carrier deciding that your record no longer matches the book of business it is trying to write. Two practical consequences. First, you usually get notice and time, so use it: shopping while still insured is far better than shopping after a gap has opened, because lapse length is rated separately. Second, do not assume the non-renewal means nobody will write you, and do not assume the surcharged renewal quote from your current carrier is representative. Nonstandard carriers exist precisely for this, and their pricing on your record can differ from each other by a wide margin. The mistake to avoid is going uninsured for a few weeks while you think about it, because that gap becomes its own rating factor.