I just tried it with ASE 11.9.2 on HP-UX 11.0, Perl 5.6.1, DBD::Sybase 0.93, and saw the bug.

I used your work-around and put the % character in the execute call:

my $sth = $dbh->prepare("select * from CAL where CAL_DS like ?");
$sth->execute($param . '%');
[download]

I confirmed that worked as expected.

Update
Removed nonsensical sentence....