If a Pokemons unburden ability activates..?

Question

Will it keep its speed if it switches out?

Answer 1

>Unburden doubles the Pokémon's Speed stat when the Pokémon's held item is lost. If there is no held item to begin with or if a held item is traded for another, Unburden will not be activated. This boost is lost if the Pokémon is switched out.

There's your answer.

Source
Hope I helped!

Answer 2

Nope.

Taken straight from Bulbapedia:

In battle
Unburden doubles the Pokémon's Speed stat when the Pokémon's held item is lost. If there is no held item to begin with or if a held item is traded for another, Unburden will not be activated.
This boost is lost if the Pokémon is switched out.

Here's the link
http://bulbapedia.bulbagarden.net/wiki/Unburden_(Ability)