During the 1980s, prior to the 486 (well, strictly speaking, prior to the discontinuing of the 486SX in the nineties), IBM PCs and compatibles had hardware floating point only in the form of an optional coprocessor. Programmers responded to this in a variety of ways.
Some programs required the coprocessor.
Some would use it if present, fall back on software floating point if not. Presumably the format of floating-point numbers would not change between the two cases.
And some ignored the coprocessor and just used software floating point.
If you know you are going to be using software floating point, you might want to format the numbers differently. For example, make the exponent plus sign exactly 16 bits, to be loaded in just one instruction, and the mantissa 32 or 64 bits.
More subtly, IEEE implements a small but clever optimization in not actually storing the leading '1' bit that will always be present in a normal, nonzero number. But if you know you are going to be using the integer multiply instruction, you might want to eschew that in favor of immediately usable data.
Did any software floating point on IBM PCs and compatibles, actually deviate from IEEE format? (As opposed to the 8-bit machines, which mostly used a non-IEEE 40-bit format.)