A number of nations had men who volunteered to fight for the papacy. There was the Corsican guard that was somewhat obviously comprised mainly of Corsicans. This unit ceased operations in 1860 at the very beginning of the process of Italian unification. The Papal Zouaves featured a wider variety of nations comprising its members, and it functioned from 1861 until 1870. The last vestige of military support from the outside was a French unit supplied by Napoleon III. When France was defeated in the Franco-Prussian War this unit was withdrawn and Rome fell to the Italians.

It must be noted that the 1870 collapse of papal military resistance is one of a number of times that the pope had lost control over Rome. The most recent such loss in 1870 was during the revolutions of 1848, when the pope had to flee. This pope was Pius IX, the very same pope that saw the 1870 collapse of his temporal power. Most of the rest of the world saw the 1870 collapse as nothing truly novel. The papacy had been displaced before, and had always been restored by one means or another. The recognition that this was a truly novel state for the papacy and Catholicism was slow to come, and became known as "The Roman Question." The papacy and the new Italian state had an uneasy standoff from 1870 until 1929, when the Lateran Concordat was signed, creating the new nation of the Vatican City and formalizing relations between that new nation and Italy.

I hope that answers your question. There were obviously those who felt otherwise, but most of the observers at the time didn't know that this particular collapse of papal temporal power was any different from previous problems in that area. The Papal States were never more than a minor regional power, and any time they engaged a major continental power it was very likely to go poorly for the papacy for a time. Generally a different major power would restore the papacy to its holdings for one reason or another. There was no real reason to believe that this would be otherwise in 1870.

As always, followup questions from OP and others are encouraged.