Jesus said we are to forgive others, but does that mean we should stay in relationships with people who are toxic and manipulative?
I am not sure which kind of relationships you have in mind. When it comes to marriage, the Bible lists unfaithfulness (Matthew 19:9) and malicious desertion (1 Corinthians 7:15) as actions that break the marriage bond and enable the other spouse to leave that relationship. Other situations can call for loving rebuke, confession and absolution to enable spouses to maintain their commitment to one another.
When it comes to friendships, there could be circumstances that warrant creating distance from people who do not treat us well. If that is the case, Christians still have biblical mandates like these to guide their actions: “Love your enemies” (Matthew 5:44), “Bless those who persecute you; bless and do not curse” (Romans 12:14), and “Get rid of all bitterness, rage and anger, brawling and slander, along with every form of malice” (Ephesians 4:31).
God bless your efforts to speak openly and honestly with people (Ephesians 4:15) and to seek their good (1 Corinthians 10:24).