From time to time, Quiet will call a supply drop for you. It seems to be identical to the one called from your iDroid.
What are the requirements for Quiet to call a supply drop for you?
Reference: Official guide book, page 302: Retrieve a supply drop ordered by Quiet (up to five times per mission/free-roaming sequence) +0.5 bound. On page 305 (same book), you get a table called Quiet's Supply Drops which tells you what she gives you depending on your bound -- there are four tiers. However, there are no indications as to why or when she does order a drop. You have to keep your eyes open. I am assuming it is when one of your items runs out.