A suppressed parish still technically exists as a parish, but is not permitted to function for some reason. No licit liturgy.
It’s not exclusively eastern; it’s not exclusively Catholic, either.
In some cases, it’s a prelude to formal closure. In others, a notice that the parish is schismatic and/or in heresy. If its suppressed, and no one is attending, it’s essentially a closed parish. If people are attending, it’s probably one of: schismatic, heretical, about to be closed, about to be reopened.
It’s often easier to just go ahead and close a parish in the Roman Rite, because it merely takes the bishop’s permission to establish a new parish. Dioceses, however, usually remain suppressed, rather than get deleted, and then are used for auxiliary bishop’s technical sees; only Rome or the synod of an ECC can suppress a diocese; the latter only one of their own.
In the ECCs, however, outside the “traditional lands” it takes both the local roman and the ECC bishop’s approval to open a new EC mission or parish… but only the EC Bishop to reopen a suppressed parish.