I can't reproduce this on Godot 3.2.3 with JPEGs generated by ImageMagick (convert -size 1x1 xc:"#fff" 1x1.jpg). However, I can reproduce this with your MRP:

godot.x11.tools.64.llvm: thirdparty/jpeg-compressor/jpgd.h:278: int jpgd::jpeg_decoder::check_sample_buf_ofs(int) const: Assertion `ofs >= 0' failed.

My minimal reproduction project: small_jpeg_import_crash.zip

file information for your MRP:

Background.jpg: JPEG image data, JFIF standard 1.01, resolution (DPI), density 96x96, segment length 16, baseline, precision 8, 1x1, components 3

file information for my MRP:

1x1.jpg: JPEG image data, JFIF standard 1.01, aspect ratio, density 1x1, segment length 16, baseline, precision 8, 1x1, components 1
1x2.jpg: JPEG image data, JFIF standard 1.01, aspect ratio, density 1x1, segment length 16, baseline, precision 8, 1x2, components 1
2x2.jpg: JPEG image data, JFIF standard 1.01, aspect ratio, density 1x1, segment length 16, baseline, precision 8, 2x2, components 1
2x3.jpg: JPEG image data, JFIF standard 1.01, aspect ratio, density 1x1, segment length 16, baseline, precision 8, 2x3, components 1
2x4.jpg: JPEG image data, JFIF standard 1.01, aspect ratio, density 1x1, segment length 16, baseline, precision 8, 2x4, components 1
4x4.jpg: JPEG image data, JFIF standard 1.01, aspect ratio, density 1x1, segment length 16, baseline, precision 8, 4x4, components 1

I can reproduce this with JPEGs generated by ImageMagick if I set the colorspace to YCbCr and use a sampling factor of 2x2:

convert -size 1x1 xc:"#fff" -sampling-factor 2x2 -colorspace ycbcr 1x1.jpg

This produces the same backtrace as the MRP.

This is happening to me also, while trying to import a .dae file with a 1x2 texture.

hello,
I want To work on this i understood the problem but i really don't known where to start .
I imported the MRP saw that it got froze at Importing assets dialog and Crashed, so I think i should start by checking code for importing project and importing assets functions but, it's hard to find.

Any help regarding this Is Appreciated.

If you can reproduce the crash, use a debugger to get a stacktrace, which will show you which files are involved.

There's a hint in #42363 (comment):

godot.x11.tools.64.llvm: thirdparty/jpeg-compressor/jpgd.h:278: int jpgd::jpeg_decoder::check_sample_buf_ofs(int) const: Assertion `ofs >= 0' failed.

You can then search which files include this file:

$ rg "jpgd.h"
thirdparty/jpeg-compressor/jpgd.cpp
29:#include "jpgd.h"

thirdparty/jpeg-compressor/jpgd.h
1:// jpgd.h - C++ class for JPEG decompression.

modules/jpg/image_loader_jpegd.cpp
36:#include <jpgd.h>

(But again a stacktrace would show you that the crash in thirdparty/jpeg-compressor/jpgd.h originates in modules/jpg/image_loader_jpegd.cpp, and would additionally give you the relevant line and further call stack for what triggers that image loader call in the editor import code.)

So, I checked the code int b = (c_x1 >> 3) * BLOCKS_PER_MCU * 64 + (c_x1 & 7); which is in file thirdparty/jpeg-compressor/jpgd.cpp on Line 2061

above value b becoming negative which eventually on the next line :
int cb10_sample = p_C0Samples[check_sample_buf_ofs(b + y0_base)];
is used to call check_sample_buf_ofs() which checks whether passed argument is positive or not
(check check_sample_buf_ofs() defination ) and closes the program when it's negative -> CAUSE OF ERROR

Then, I tried to read the function in which this whole thing is implemented and found out that it is uint32_t jpeg_decoder::H2V2ConvertFiltered() Fuction.

now i am really stuck on what to do next because i don't see anything wrong in the implementation.

If i am missing something. I'm Happy to learn it.