To check what files are being used by a process, you can use lsof with option -p.
Example:
# lsof -p 2791
COMMAND PID USER FD TYPE DEVICE SIZE NODE NAME
syslogd 2791 root cwd DIR 8,2 8192 2 /
syslogd 2791 root rtd DIR 8,2 8192 2 /
syslogd 2791 root txt REG 8,2 35712 1046656 /sbin/syslogd
syslogd 2791 root mem REG 8,2 52152 523300 /lib/libnss_files-2.3.2.so
syslogd 2791 root mem REG 8,2 1572440 1291815 /lib/tls/libc-2.3.2.so
syslogd 2791 root mem REG 8,2 106912 523267 /lib/ld-2.3.2.so
syslogd 2791 root 0u unix 0xf6439880 2746 /dev/log
<snip>
In Solaris, you can also use “pfiles <pid>”.