Different legislatures have different rules. And also specific legislatures have different rules for different activities. 

https://en.wikipedia.org/wiki/Filibuster
https://en.wikipedia.org/wiki/Filibuster_in_the_United_States_Senate

And indeed, they may change the rules over time.

https://en.wikipedia.org/wiki/Nuclear_option

In some legislatures the rule for some kinds of debate is that as long as a speaker continues to speak, he or she cannot be stopped. There may be rules about breaks, what happens if the legislature wants to take a rest, if the speaker can temporarily give the floor to somebody else then get it back, etc. and etc. Or, the speaker may be required to stand while speaking until he/she gives up.

But, in some cases, as long as the person doing the filibuster continues, the rules say the debate can't be closed. And they don't even have to talk about the issue at hand. People have been known to read the phone book, sing, etc.

http://mentalfloss.com/article/49360/5-famous-filibusters

So, if the speaker has more stamina than the legislature, or the public or press is on his/her side and shames the legislature, it is potentially possible for a single person to stop a legislature from taking a specific action.

It is by no means the only delaying tactic that has been used at times.

https://www.americanprogress.org/issues/general/news/2010/09/28/8328/minority-rules/

But every such tactic has the potential of working, or of backfiring. If other members of the legislature, or the public or the press, have a favorable opinion then it can work. If they have an unfavorable opinion, then the delaying persons can find they have lost all support. Most politicians in legislatures with meaningful debate will have at least some degree of concern for such support. And the same is true of methods used to close off the delays.