what happens if the owner decides to remove it? Does that mean maven can't find the external project and my app won't run anymore?
No. Artifacts on mavenCentral are not allowed to be removed, not even by the owner. So that will not happen.
See Joel Orlina's (Sr. developer at Sonartype) post at https://issues.sonatype.org/browse/OSSRH-13636
Sonatype policy prohibits the removal or other modification of artifacts once they've been published to Central. The reasoning behind this is that if the artifact changes after publication, any builds that already depend on it will break
Central referring to mavenCentral
The reasons he states is very valid and seems to be exactly what made you wonder.
Also see Removing an artifact from Maven Central