Context : The stellar content of Galactic open clusters is gradually depleted during their evolution as a result of internal relaxation and external interactions .
The final residues of the long-term evolution of open clusters are called open cluster remnants .
These are sparsely populated structures that can barely be distinguished from the field .

Aims : We aimed to characterise and compare the dynamical states of a set of 16 objects catalogued as remnants or remnant candidates .
We employed parameters that are intimately associated with the dynamical evolution : age , limiting radius , stellar mass , and velocity dispersion .
The sample also includes 7 objects that are catalogued as dynamically evolved open clusters for comparison purposes .

Methods : We used photometric data from the 2MASS catalogue , proper motions and parallaxes from the GAIA DR2 catalogue , and a decontamination algorithm that was applied to the three-dimensional astrometric space of proper motions and parallaxes ( \mu _ { \alpha } , \mu _ { \delta } , \varpi ) for stars in the objects ’ areas .
The luminosity and mass functions and total masses for most open cluster remnants are derived here for the first time .
Our analysis used predictions of N -body simulations to estimate the initial number of stars of the remnants from their dissolution timescales .

Results : The investigated open cluster remnants present masses ( M ) and velocity dispersions ( \sigma _ { v } ) within well-defined ranges : M between \sim 10 - 40 M _ { \odot } and \sigma _ { v } between \sim 1 - 7 km s ^ { -1 } .
Some objects in the remnant sample have a limiting radius R _ { \textrm { lim } } \lesssim 2 pc , which means that they are more compact than the investigated open clusters ; other remnants have R _ { \textrm { lim } } between \sim 2 - 7 pc , which is comparable to the open clusters .
We suggest that cluster NGC 2180 ( previously classified as an open cluster ) is entering a remnant evolutionary stage .
In general , our clusters show signals of depletion of low-mass stars .
This confirms their dynamically evolved states .

Conclusions : We conclude that the open cluster remnants we studied are in fact remnants of initially very populous open clusters ( N _ { 0 } \sim 10 ^ { 3 } -10 ^ { 4 } stars ) .
The outcome of the long-term evolution is to bring the final residues of the open clusters to dynamical states that are similar to each other , thus masking out the memory of the initial formation conditions of star clusters .