gdb をアタッチして backtrace を実行すると、私の理論がほぼ裏付けられます...
$ gdb /opt/our_process pid
...blah blah blah...
(gdb) bt
#0 0x0000003f27adae60 in __write_nocancel () from /lib64/libc.so.6
#1 0x0000003f27a71583 in _IO_new_file_write () from /lib64/libc.so.6
#2 0x0000003f27a7144a in _IO_new_file_xsputn () from /lib64/libc.so.6
#3 0x0000003f27a49531 in buffered_vfprintf () from /lib64/libc.so.6
#4 0x0000003f27a4449e in vfprintf () from /lib64/libc.so.6
#5 0x0000003f27a4f03a in printf () from /lib64/libc.so.6
...out process's stack...
そして、シェルターが提案したように、straceもうまくいくようです...
$ strace -p 27689
Process 27689 attached - interrupt to quit
write(1, "some_text"..., 293