  In partial action theory, a pertinent question is whenever given a partial
(co)action of a Hopf algebra A on an algebra R, it is possible to construct an
enveloping (co)action. The authors Alves and Batista, in [2],have shown that
this is always possible if R has unit. We are interested in investigating the
situation where both algebras A and R are nonunitary. A nonunitary natural
extension for the concept of Hopf algebras was proposed by Van Daele, in [11],
which is called multiplier Hopf algebra. Therefore, we will consider partial
(co)actions of multipliers Hopf algebras on algebras not necessarily unitary
and we will present globalization theorems for these structures. Moreover,
Dockuchaev, Del Rio and Sim\'on, in [5], have shown when group partial actions
on nonunitary algebras are globalizable. Based in [5], we will establish a
bijection between group partial actions on an algebra R not necessarily unitary
and partial actions of a multiplier Hopf algebra on the algebra R.
