If I am reading your question correctly you are asking once Italy was taken in World War 2 what happened to the allied troops there. The answer is Italy never was taken throughout the war and fighting for it continued till the end.

After the invasion of Normandy and later the Dragoon assaults Italy became a much lesser priority with a focus on the Western front. As the war went on many units were taken from the Italian command to be sent to fight in France for example a French Corps that joined the French First Army.

The territory of northern Italy made offensive warfare very difficult. The allies continued trying to push north but we're slowed and stopped in many cases in what turned into a bloody brawl between the forces.

After Operation Cobra and the resulting drive across France it was seen that the forces in Italy would not beat the forces in France to taking Germany and after this they mainly worked to tie down German forces. In the end the Italian campaign late in the war did provide a valuable service of engaging large German forces letting the rest of the Allied armies drive into German with less opposition.

Source: The War in Italy, 1943-1945 Richard Lamb