The State of Wei was a State during the Spring and Autumn period, and it was the one that had existed for the longest. Even after the First Emperor of Qin destroyed the other States, he didn't destroy the State of Wei.
This wasn't because the First Emperor of Qin didn't have the power to destroy the State of Wei – after all, he had destroyed the powerful six states, so how could he not have the power to destroy the tiny State of Wei?
It was because the State of Wei had already been a subsidiary of the Qin State, and their relationship had been quite good. Another reason was that the State of Wei had been destroyed by the Wei State and only had a few cities left, making it alive in name only.
[TLN: Both states have different characters but are both 'Wei' in pinyin]
Even though the State of Wei existed in name only, the First Emperor of Qin had still allowed it to exist; when the second Qin Emperor rose to power, he got rid of the State of Wei in name.