The Mishna in chapter 2 of M'ila outlines when the use of a sacrificial offering for one's own purposes, by accident, engenders the requirement to bring a sin-offering. Most kodshe kadashim ("most holy" offerings) can engender such a requirement if the use was before "they went out to the ash area", meaning that they were burnt on the altar and (the next morning as every morning) some ash was removed from the altar — or, some explain, that the altar was emptied of ashes, which occurred less often.
Why until the ash was removed from the altar? The standard is "until its command is fulfilled" but (1) taking ashes each morning from the altar is unrelated to, and may not even contain the ashes of, any particular offering, and (2) emptying the altar of ashes is no command at all and was done when convenient.