Пусть убивает.
в кроне:
*/1 * * * * ~/tmp/check_tomcat.sh >> ~/tmp/check_tomcat.sh.log 2>&1
cat ~/tmp/check_tomcat.sh
#!/bin/bash
if [ $( ps -ef|grep tomcat|grep java|wc -l ) -eq 0 ]
then
echo "tomcat process not found, try to start"
service tomcat start
else
echo "tomcat process found"
fi