Is it possible to interpret this as "Gurlak is afraid to die suddenly"? And if not, how would you express that?
I believe it’s not possible to interpret it like that — I think that adverbials such as pay' only apply to the entire sentence, i.e. to the HeghvIp ghurlaq, and that you can‘t take pay Hegh and then tack -vIp onto that sentence to make it "He is afraid of he dies suddenly".
Instead, I think you would have to say something like chaq pay‘ Hegh ghurlaq. ghaH ghIj DuHvam. „Perhaps Gurlak will die suddenly. This possibility scares him.“
Or at least to that entire phrase. If you have a sentence made up of multiple phrases then it might apply to the verb immediately following it and not the entire sentence. However, I don't think you can apply the adverb to a suffix on the verb. When in doubt always split it into two separate sentences. Klingon can create some very complicated sentences, but seems to prefer shorter simpler sentences when it helps clarify the point.