It all depends on how you have designed your page and what content you have in your page and how it is arranged?
There is no one answer because it depends on the design and the content.
If you have designed a rigid looking page and then placed it in a fluid page then things will break unless you have made arrangements for elements to reflow as the page shortens.
You can't expect a graphical horizontal menu to break to two or three lines and still work if it is full of matching graphics. If it's just text you can let it wrap as required with no problem.
If you have fixed with elements like images in fluid columns then you would probably need to set min-widths as appropriate.
In essence you don't just design a site and expect it to work everywhere - you design it to work everywhere. That means making decisions all along the way on how things are going to work and "what happens if....." .
If you have a link to the site then perhaps we can make some more specific comments:)