Italian troops were force-ably disarmed and the troops captured by the Germans were given a choice to keep fighting with the Germans or go to concentration camps/forced labour. About 94,000 Italians accepted and the remaining 710,000 were designated Italian military internees and were transported as slave labour to Germany. Some Italian troops in the Balkans joined the Yugoslav and Greek Resistance.[1]

An interesting one where the italians refused to disarm was in Cephalonia, Greece where they gave up their heavy artillery but refused to give up their arms and told the Germans to leave the island. The Germans proceeded take the island by force and the Italians ended up losing and surrendering, they were then all executed for treason. Side note: there's a movie based on it called Captain Corelli's mandelin, I wouldn't trust it for historical authenticity but it's entertaining

[1] O'Reilly, Charles T., Forgotten battles: Italy's war of liberation, 1943–1945. Illustrated ed., Publisher: Lexington Books, Year: 2001, ISBN 0-7391-0195-1, p. 14