Other forms: unsolicitedly
Something unsolicited was not asked for and possibly not wanted. Unsolicited calls and advice come whether we want them or not.
One very common use of this word is in discussing "unsolicited advice" or feedback, which definitely has a negative spin. If someone is butting into your business, telling you what you should do, they're giving unsolicited advice. Junk mail is unsolicited. Phone calls trying to sell you something are unsolicited. Unsolicited seems negative, but it can be used positively. If you give compliments that are unsolicited, then you offer them spontaneously and honestly — that's something people like.