By itself, the phrase "as of" merely asserts that a certain fact is true at one specific time. So in your example, the person was unemployed at the time the statement was written.
Depending on the context, a change from a previous state might be inferred. For example, if your boss writes you a letter saying that "as of your receipt of this letter, you are unemployed", the letter is firing you and you no longer have a job. Similarly, the phrase can be used to announce a future change before it takes effect: "As of next week, our company policy will be [...]."
The phrase can also be used for statements that were true at some time in the past but may no longer be true at the time they are read. "The army was still holding the enemy off at the pass as of two nights ago, but the general did not think they could last past noon yesterday." Or, to circle back to your example sentence fragment, you might see this in an editor's note on an newspaper article about unemployment: "The author of this article was unemployed as of the time of writing, but has since started a job with company X." (This would perhaps be a little unusual though, since generally "as of the time of writing" refers to the writing of the current text, rather than some other text.)