come out of something—
1. leave the place (where smth. has been fixed):
- The screw was rusty and wouldn’t come out of the wall.
2. (of stains, etc.) disappear; be removed from smth. (with cleaning):
- Do you think these ink-marks will come out of my dress if I boil it?
go out of something—
1. (of passion, tension, etc.) become less marked in smth.; disappear from smth.:
- As time went by, the fury went out of his parliamentary speeches.
2. be no longer in fashion, business, etc.:
- As from next Wednesday the oil and petrol pool, which has operated since the war, will go out of business.
Note: Neither expression correlates in meaning with the phrase run out of something—have no further supply of smth.:
- He had several forced landings, the first when he ran out of fuel over Syria.
See also: walk out of something / walk out on something.