No process that violates the First Law of Thermodynamics has ever been found to take place. But, there are processes which do not defy the First Law of Thermodynamics but still do not take place in nature.
That is, if a process is ruled out by the First Law of thermodynamics, it will not take place. But, if it isn't then too, it is not neccesary that the process be feasible.
For example, the amount of heat that will be released water if it solidifies at, say 300K and 1 atm. can be calculated by using the first law. And it predicts that water will solidify at these conditions if it releases that much heat. But we know that ice is not formed at these conditions.
This means there might be another law of physics that will provide us the ability to predict whether a process permitted by the first law of thermodynamics will actually take place or not.
That law is the Second Law of Thermodynamics.