Up until now, we've mostly been talking about things that have happened or changed in the course of events. We will now learn some simple grammar to express a lack of change.
「まま」, not to be confused with the childish expression for "mother" （ママ）, is a grammatical phrase to express a lack of change in something. Grammatically, it is used just like a regular noun. You'll most likely hear this grammar at a convenience store when you buy a very small item. Since store clerks use super polite expressions and at lightening fast speeds, learning this one expression will help you out a bit in advance. (Of course, upon showing a lack of comprehension, the person usually repeats the exact same phrase... at the exact same speed.)
In other words, the clerk wants to know if you'll take it just like that or whether you want it in a small bag. 「宜しい」, in case I haven't gone over it yet, is simply a very polite version of 「いい」. Notice that 「まま」 grammatically works just like a regular noun which means, as usual, that you can modify it with verb phrases or adjectives.
Ok, the translation is very loose, but the idea is that it's in an unchanged state of being half-eaten and you can't just throw that out.
Here's a good example I found googling around.
Hint: The 「いさせる」 is the causative form of 「いる」 meaning "let/make me exist".
Finally, just in case, here's an example of direct noun modification.
The verb 「放す」 meaning "to set loose", can be used in various ways in regards to leaving something the way it is. For instance, a variation 「放っとく」 is used when you want to say "Leave me alone". For instance, you might use the command form of a request （くれる） and say, 「ほっといてくれ！」(Leave me alone!). Yet another variant 「ほったらかす」 means "to neglect".
The grammar I would like to discuss here is the 「っぱなし」 suffix variant. You can attach this suffix to the stem of any verb to describe the act of doing something and leaving it that way without changing it. You can treat the combination like a regular noun.
As usual, you can click the [EX] link after looking up the word at the WWWJDIC to see examples. In fact, here's a direct link to examples of this grammar. As you can see by the examples, this suffix carries a nuance that the thing left alone is due to oversight or neglect. Here are the (simple) conjugation rules for this grammar.