  Aims. GAIA delivers the positions and velocities of stars at unprecedented
precision. Therefore, for star clusters, there exists much higher confidence in
whether a specific star is a member of a particular group. However, membership
determination is still challenging for young star clusters. At ages 2-10 Myr,
the gas is expelled, leading to cluster expansion, while many former members
become unbound. We aim to assess the accuracy of the methods used to
distinguish between bound and unbound cluster members. After identifying the
most suitable technique, we wish to understand which of the two populations
provides more insights into the initial configuration and the dynamic history
of a cluster. Methods. Here, we perform N-body simulations of the dynamics of
such young star clusters. We investigate how cluster dynamics and observational
limitations affect the recovered information about the cluster from a
theoretical perspective. Results. We find that the much-used method of distance
and velocity cutoffs for membership determination often leads to false
negatives and positives alike. Often observational studies focus on the stars
remaining bound. However, they quickly lose the memory of the pre-gas expulsion
phase due to interactions with other cluster members. Our study shows that the
unbound stars hold the key to charting a cluster's dynamic history.
Backtracking unbound stars can provide the original cluster size and determine
the time of gas expulsion. This information is lost in the bound population. In
addition, former members are often better indicators for disc lifetimes or
initial binary fractions. We apply the backtracking analysis, with varying
success, to the clusters: Upper Scorpius and NGC 6530. For highly substructured
clusters such as Upper Scorpius, backtracking to the individual subcluster
centres will provide better results in the future (abridged).
