[jdk21u-dev] RFR: 8333108: Update vmTestbase/nsk/share/DebugeeProcess.java to don't use finalization

[Goetz Lindenmaier]

I backport this for parity with 21.0.6-oracle.

-------------

Commit messages:
 - Backport b3e29db14466ccc64a2815224ecefab4cec4c775

Changes: https://git.openjdk.org/jdk21u-dev/pull/971/files
  Webrev: https://webrevs.openjdk.org/?repo=jdk21u-dev&pr=971&range=00
  Issue: https://bugs.openjdk.org/browse/JDK-8333108
  Stats: 42 lines in 6 files changed: 16 ins; 21 del; 5 mod
  Patch: https://git.openjdk.org/jdk21u-dev/pull/971.diff
  Fetch: git fetch https://git.openjdk.org/jdk21u-dev.git pull/971/head:pull/971

PR: https://git.openjdk.org/jdk21u-dev/pull/971