There is a utility called sybdumptran that allows to make a transaction log backup despite the non working sybase server.
Take a look at the following SQL code:
DISK INIT NAME ='MyDbDataDev', PHYSNAME = '/opt/sap/databases/MyDbDataDev.dat', SIZE=10240 GO
DISK INIT NAME ='MyDbLogDev', PHYSNAME = '/opt/sap/databases/MyDbLogDev.dat', SIZE=2560 GO
CREATE DATABASE MyDb ON MyDbDataDev = '20M' LOG ON MyDbLogDev = '5M' GO
DUMP DATABASE MyDb TO '/home/dumps/MyDb_full.dmp' WITH INIT GO
USE MyDb GO
CREATE TABLE TEST(info char(30)) GO
INSERT INTO TEST VALUES('Before the 1st log dump') GO
DUMP TRAN MyDb TO '/home/dumps/MyDb_log_1.dmp' GO
INSERT INTO TEST VALUES('Never dumped') GO
SHUTDOWN
As you see a new database on new devices has been created. Next we took a full backup, next user inserted one record, next the transaction low was dumped, next the user continued to insert the next record and then something went wrong and server stopped! Now you will see how to take a log dump despite stopped server: