According to the limits page on the SL wiki http://wiki.secondlife.com/wiki/Limits#Textures Profile pictures are expected to be square.
Currently, when you resize the resident info pane of an IM window, the image stretches sideways, or compresses sideways to fill the available space.
I suggest that the image should scale in both directions, to maintain it's aspect ratio, while still shrinking of expanding to fill the available sideways space.
Since the images contain up to 300px by 300px (600x600 on the web), it seems that there should be plenty of available resolution to scale the image while maintaining the aspect ratio of the image.
Catznip R9.0.11 Apr 14 2014 00:12:31 (Catznip Beta)
You are at 207.7, 133.5, 1,402.1 in Moraenae located at sim10484.agni.lindenlab.com (188.8.131.52:13018)
(global coordinates 262,608.0, 236,933.0, 1,402.1)
Second Life RC BlueSteel 14.03.28.288552
CPU: Intel(R) Core(TM)2 Quad CPU Q9650 @ 3.00GHz (3000.06 MHz)
Memory: 4094 MB
OS Version: Microsoft Windows 7 64-bit Service Pack 1 (Build 7601)
Graphics Card Vendor: NVIDIA Corporation
Graphics Card: GeForce GTX 275/PCIe/SSE2
Windows Graphics Driver Version: 9.18.0013.3523
OpenGL Version: 3.3.0
RestrainedLove API: RLV v2.8.0 / RLVa v1.4.10a
libcurl Version: libcurl/7.21.1 OpenSSL/0.9.8q zlib/1.2.5 c-ares/1.7.1
J2C Decoder Version: OpenJPEG: 1.4.0, Runtime: 1.4.0
Audio Driver Version: FMOD Ex 4.44.17
Qt Webkit Version: 4.7.1 (version number hard-coded)
Voice Server Version: Vivox 4.5.0009.17865
Built with MSVC version 1600
Packets Lost: 579/566,938 (0.1%)