Alexi is murdered during the Coup.
Answer from the Mayhew Family is a written note found in Dishonored 2.
Transcript[]
We are devastated since our Alexi's death, but we found some comfort knowing that you managed to escape and that there may yet be hope for Dunwall and our Empress. Thank you for your kind words.
We're ashamed to say that we won't wait for your return though. One morning, all the bread in Gideon's bakery was turned to ashes; on another, the wool yarns in my haberdasher shop were full of snails and slugs. There's a curse on the city, and I'm not even talking about the Hatter gang who now rule over our streets.
Anyway, we're returning to our old home in Potterstead, where Alexi grew up. Good luck to you.
Paulina Mayhew
Location[]
It can be found in the guest quarters on the Dreadful Wale just before the mission The Grand Palace. An alternative note is found if playing as Emily.