Does a reaction cease when it reaches dynamic equilibrium?
No, it doesn't.
What actually happens is that, at dynamic equilibrium the rate at which the reactants react to form products(in the forward reaction), is equal to the rate at which the products form the reactants(in the backward reaction).
In fact, the word dynamic means that the reaction does not cease, and the word equilibrium means that the forward reaction is going on at the same pace as the backward reaction.
It's different from static equilibrium whereby the reaction has stopped(maybe comparable to the endpoint of a reaction, ...i say maybe...)
Plus Fact :
At dynamic equilibrium the reaction only appears to have ceased, because to no visible changes occur. Whereas the reaction is going on.