Car stopped while driving

My 2001 VW Passat got a new battery recently, after few days of this change my car started stopping when I slow down some time, the battery is completely down the indicators won’t work and I couldn’t lift the window glass up. When I jumpstarted it everything is normal, there is no trouble for 2days (so far :)) I was wondering what could have happen and as it is very likely to happen again.
If I had a bad batter will it stop a running car?
If it is issue with alternator why would it stop while running?
Thanks for your inputs