There is a significant difference between actually zero and merely very close to zero. Does Bayesian reasoning strike a difference between zero and asymptotica

There is a significant difference between actually zero and merely very close to zero. Does Bayesian reasoning strike a difference between zero and asymptotically zero? It's my understanding that probability density functions are a method to dodge the problem in the frequentist approach, so I'm assuming the Bayesian approach also claims anything with probability limes 0 is impossible and just makes sure not to consider such cases.