Wash. Rev. Code § 36.08.050
Every county which is thus enlarged by territory taken from another county shall be liable for a just proportion of the existing debts of the county from which such territory is stricken, which proportion shall be paid by the county to which such territory is transferred at such time and in such manner as may be agreed upon by the boards of county commissioners of both counties: PROVIDED, That the county to which the territory is transferred shall not be liable for any portion of the debt of the county from which the territory is taken, incurred in the purchase of any county property, or the construction of any county building then in use or under construction, which shall fall within and be retained by the county from which the territory is taken.
RCW 36.08.050