This is a disinformation narrative often used in relation to the Eastern Partnership (EaP) initiative, claiming that this is an anti-Russian instrument and a mechanism to control its members.
In fact, the EaP was established as a specific Eastern dimension of the European Neighborhood Policy, which contains both a bilateral and multilateral track. This is a joint policy initiative, based on voluntary participation, which aims to strengthen relations between the European Union, its member states and its six Eastern neighbours: Armenia, Azerbaijan, Belarus, Georgia, Moldova and Ukraine. According to the official website, it was released on 7 May 2009 by the Joint Declaration of the Prague Eastern Partnership Summit.
The concept of this volountary partnership is "more for more" - those countries wanting to develop closer relations with the EU may do so while other countries choose other levels of contact. The best examples of the diversity in the EaP is the paths chosen by the differnet countries themselves. See the EaP Summit December 2021 results here.
So far, none of these countries has announced its intention to leave the Partnership, except Belarus, which has suspended its participation on 26 June 2021, after the EU imposed sanctions on Lukashenka's regime for the pressure on its own population.
See here a similar case about EaP as a mechanism to control members and here a case claiming that EaP was conceived from the beginning as a geopolitical trap.