I have an SPST momentary tactile switch and want the pulse, whatever length, to be extended to 500ms (unless of course the button is pressed for longer than 500ms but we can ignore that if we hold the pulse form the rising edge). I don't know if there is a single IC to hold a pulse like this or if I can do it with passive components like resistors and capacitors.
You can do this with CMOS inverter, a diode , cap and resistor to discharge the cap slowly.
It's called a monostable Multivibrator or 1 SHOT and there are many other ways to accomplish this.
But the typical IC's are state driven, while some are edge driven. They may be re-triggerable or non-retriggerable and the latter is what you wanted.
The LTC®6993-1 is a monostable multivibrator (also known as a “one-shot” pulse generator) with a programmable pulse width of 1µs to 33.6 seconds, with the non-retrig option and rising edge option.
Easy 0.6s with 6 in one IC
As much as it pains me to say this, a CMOS 555 will do exactly what you want. The standard circuit will give a constant output pulse width for any input pulse shorter than the timeout period. If the input still is low, the output will remain high until the input goes high; then the output will go low immediately. Retriggers caused by switch bounce during the timing period are ignored. The Micrel MIC1555 is in a 5-pin SOT-23 package. 1 chip, 1 R, 1 C (plus decoupling).