I tried to reproduce it in two cases:

0. environment

    Firefox 3.0.10
        NoScript 1.9.2.6
        Session Manager 0.6.5
        Web Developer 1.1.6
    Linux Kernel 2.6.23.17-88.fc7 (Fedora Core 7)

1. small free space case

    $ df .
    Filesystem           1K-blocks      Used Available Use% Mounted on
    -                      5493972   5493760       212 100% /home

    I tried to download the following link:
    http://www.kernel.org/pub/linux/kernel/v2.6/linux-2.6.22.9.tar.gz

    Firefox asked "What should Firefox do with this file?". I chose
    "Save File" radio button and clicked "OK" button.

    The download manager didn't show up as expected and
    Firefox crashed with a message box "The Application Crashed".

2. larger free space case

    $ df .
    Filesystem           1K-blocks      Used Available Use% Mounted on
    -                      5493972   5469848     24124 100% /home

    I tried to download the following link:
    http://www.kernel.org/pub/linux/kernel/v2.6/linux-2.6.22.9.tar.gz

    Firefox asked "What should Firefox do with this file?". I chose
    "Save File" radio button and clicked "OK" button.

    The download manager showed up and the downloading was in progress.

    I filled the free space while downloading.
    $ dd if=/dev/zero of=padding.2

    Firefox warned with a message box:
        There is not enough room on the disk to save
        /home/cchen/Desktop/linux-2.6.22.9(2).tar.gz.part.

        Remove unnecessary files from the disk and try again, or try saving in a
        different location.

    I removed the free space padding.
    $ rm padding.2

    I closed the message box.

    The download was non-responsive. The pause and cancel buttons
    didn't respond to mouse clicks. I right-clicked to popup a menu.
    The menu items seemed to work except for "Pause" and "Cancel".
    The download halted:
        linux-2.6.22.9(2).tar.gz
        53 minutes remaining - 1.5 of 54.3 MB (11.6 KB/sec)

    I went to kernel.org and tried to download the following link:
    http://www.kernel.org/pub/linux/kernel/v2.6/linux-2.6.22.9.tar.gz.sign

    The new download succeeded with a reminder from right bottom of the window:
        Downloads Complete
        All files have finished downloading.
    But it was not seen in the download manager.

    I restarted Firefox. Firefox warned with a message box:
        There is not enough room on the disk to save
        /home/cchen/Desktop/linux-2.6.22.9(2).tar.gz.part.

    $ ll ~/Desktop/linux-2.6.22.9\(2\).*
    -rw------- 1 cchen cchen 11087872 2009-05-13 14:35 /home/cchen/Desktop/linux-2.6.22.9(2).tar.gz
    It seems that Firefox resumed downloading somewhere (from 1.5MB to 11MB).

    I cleaned it up.
    $ rm ~/Desktop/linux-2.6.22.9\(2\).*

    I closed the above message box.

    The previous downloaded linux-2.6.22.9.tar.gz.sign showed up in
    the download manager.

    I removed linux-2.6.22.9.tar.gz.sign from the download manager.

    The download was still non-responsive. The pause and cancel buttons
    didn't respond to mouse clicks. I right-clicked to popup a menu.
    The menu items seemed to work except for "Pause" and "Cancel".
    The download halted:
        linux-2.6.22.9(2).tar.gz
        Unknown time remaining - 0 bytes (0 bytes/sec)