HI,
I'm using Steam on Fedora and it exits while I'm downloading a game (don't know if it'll happen even if I wasn't downloading a game)
Here is the message in a terminal :
/home/USER/.local/share/Steam/steam.sh : ligne 755 : 11311 Erreur de segmentation (core dumped)$STEAM_DEBUGGER "$STEAMROOT/$PLATFORM/$STEAMEXE" "$@"

System information:

Operating System Version:
"Fedora release 20 (Heisenbug)" (64 bit)
Kernel Name: Linux
Kernel Version: 3.12.5-302.fc20.x86_64
X Server Vendor: Fedora Project
X Server Release: 11404000
X Window Manager: GNOME Shell
Steam Runtime Version: steam-runtime-release_2013-10-23

Video Card:
Driver: X.Org Gallium 0.4 on AMD RV710

Driver Version:  3.0 Mesa 9.2.5
OpenGL Version: 3.0
Desktop Color Depth: 24 bits per pixel
Monitor Refresh Rate: 59 Hz
VendorID:  0x1002
DeviceID:  0x9553
Number of Monitors:  1
Number of Logical Video Cards:  1
Primary Display Resolution:  1366 x 768
Desktop Resolution: 1366 x 768
Primary Display Size: 13,54" x 7,64"  (15,51" diag)
                                        34,4cm x 19,4cm  (39,4cm diag)
Primary VRAM Not Detected