Resupply gets from Onion Valley over Kearsarge Pass, and up to the JMT one of three ways:
1) On your back. You hike down to OV and either pick it up at the OV Pack Station (see #3) or hitch into Independence to pick it up at the post office there. Reverse your steps to the JMT.
Addendum: Just spoke to the Mt Williamson Hotel. The only grocery store in Independence has indeed recently closed; If you need something you'll have to take the local M-F bus service into Bishop. There are only 2 eateries left; a Subway (7 days a week), and the French restaurant, which is "usually" open on weekends plus a few weekdays, but closed at least Monday and Tuesday. The hotel includes a hot breakfast. They'll hold resupply boxes. A shuttle to Onion Valley - for guests only - is another $45.
2) On a friend's back. Some poor, demented soul loves you enough (or is planning to join your hike) to climb the 2700 feet from OV to the JMT/KP/Charlotte Lake trail junction and camp there until you come along. This person becomes your new best friend and you shower them with praise and cash.
3) You hire Sequoia-King Pack Trains to meet you at said four-way trail junction with your resupply package. This gets really expensive, but if there are enough of you together, you can split the cost. They also run the Onion Valley Pack Station (see #1). For details, pricing, and procedures, email Ms. Dee Berner at Sequoia Kings Pack Train at email@example.com or call 760-387-2627. Their website is http://horse-pack-trips.gordonsguide.com/sequoia/index.cfm
4) OK, I suppose you could try for a helicopter drop as a 4th method, but just the permitting alone would bankrupt you.