First, a string does not have its own context, it's a regular expression, therefore if there isn't a matching closing quote until EOF, it's not an unterminated string. It plainly *isn't* a string.
Second, the string lexer searches for either the regexp '[^"\\]' (any character except a double quote or a backslash) or the regexp '\\.', that is, a backslash followed by an "any character" meta. But the "any character" meta does NOT match a newline. The consequence is that a '\' followed by a newline cancels the matching, and the whole thing is not considered a string.
Isolated double quotes are then plain ignored as many other characters.
An example illustrating both cases:
```
default
{
state_entry()
{
string msg = "Hello, Avatar!";
llOwnerSay"(msg); // the opening quote will be ignored
// the following backslash at EOL cancels the previous double quote: \
llOwnerSay(llGetKey(")); // Unterminated string; unmatched so ignored.
}
}
```