I was wondering how does a 6502 processor knows when to stop the Fetch-Decode-Execute-Update cycle
Suppose I have a few lines of instruction say:
LDA $01
ADC $02
STA $0671
I get the program execution up to the first three instruction, but how does the processor knows after executing the third instruction here that it has to stop?
I searched a bit about it and found that in general, the program tells the O.S that is has executed successfully after which the O.S updates the Program counter to the next address of the next program. But I am not sure how this works in a 6502 processor.

Basically I am trying to make a 6502 emulator and wants to understand the termination logic for terminating the instruction fetch-decode-execute loop. Should I simply add a special instruction at the end of the program, and stop my loop when I encounter it? Or is there any separate instruction to halt the processor execution cycle.

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http://WilsonMinesCo.com/ lots of 6502 resources
The "second front page" is http://wilsonminesco.com/links.html .
What's an additional VIA among friends, anyhow?

For an emulator, using BRK is probably easiest.

Next easiest, perhaps, is for the emulator to use the stack pointer value to recognise a final RTS as exiting from the program.

As noted, a real 6502 doesn't have a way to stop running. So a very faithful emulator will emulate that: perhaps by emulating a system which has a monitor program, so the user will use the monitor to load and run a program, and the program will return to the monitor.

Another simple idiom which you can use on any system is a branch-to-self or jump-to-self which ends the program in a tight loop. This is workable on any system which allows you to reset (or interrupt) the CPU.