Either one or both partners decided to split up or to deeply consider splitting up. This means that trust will need to be re-established. In fact, we could just say "established," because there is no way to go back to the time when both partners took for granted that the relationship would last forever.
Instead of both partners saying that the relationship will never end, they can commit to telling each other when they are experiencing issues or doubts. Instead of committing to forever, they can commit to honesty and authenticity.
Couples need to have a strong sense of WHY they want to do the hard work of reconciling. Some common motivators are religious values, having an intact home for the kids and a longstanding deep history together.
When there is a complete lack of physical chemistry/attraction, attempts at reconciliation are likely doomed from the start, unless the couple agrees on a friendship-based marriage without sex (or an open marriage).
If, however, there is sexual and physical chemistry, even that waxes and wanes, between the partners, then a romantic relationship is likelier to be rekindled.
Under no circumstances should a couple try to reconcile if BOTH cannot see how they contributed to the issues in the marriage, even if one’s contribution was ignoring/enabling the other’s problem behavior.
If both parties cannot own their unique role in the marital problems, then reconciling will never truly work.
If you do not share similar values on a deep level, then leave well enough alone and stay separated. However, if you and your partner have experienced a deep empathic rupture BUT still feel you view the world very similarly, you are likelier to be able to reconcile successfully.
To summarize: if you respect their views, you should try again. If you do not respect or understand where they come from (across a range of major life arenas), do not.