Subduction of the plate carrying the landmasses.
Subduction takes place at the boundaries of tectonic plates. One plate slides beneath the other. If the plate that is going down is carrying a landmass, that landmass will go down with the plate.
An example: the Torres islands are sinking below the ocean, because the plate they are on is carrying them down.
Comparing the role of absolute sea-level rise and vertical tectonic motions in coastal flooding, Torres Islands (Vanuatu)
Since the late 1990s, rising sea levels around the Torres Islands
(north Vanuatu, southwest Pacific) have caused strong local and
international concern. In 2002–2004, a village was displaced due to
increasing sea incursions, and in 2005 a United Nations Environment
Programme press release referred to the displaced village as perhaps
the world’s first climate change “refugees.” We show here that
vertical motions of the Torres Islands themselves dominate the
apparent sea-level rise observed on the islands. From 1997 to 2009,
the absolute sea level rose by 150 + /-20 mm. But GPS data reveal that
the islands subsided by 117 + /-30 mm over the same time period,
almost doubling the apparent gradual sea-level rise...In addition, large
subduction zone earthquakes can cause nearly instantaneous vertical
movements of up to several meters (see, for example refs. 12–15). The
Torres Islands, which are located very near the plate interface, are
likely to be affected by both sudden and slow vertical motions over
different time scales.
These islands are currently sinking by a centimeter a year! The article notes that this has not been a steady process but that landmasses near these plate boundaries can suddenly move up or down during earthquakes.