Slam valve pattern

Something I've seen a sprinkling of times over the past few decades is slam valve type code where there is a contrived value which decrements/increments to force a loop to exit once a certain value has been breached or where a number of iterations have passed.

A bit abstract for you?

Some concrete examples:

File read

In this case, a file is being read in a data factory overnight so needs to be processed by a certain time in order for the system to be available in the morning. N.B. it doesn't matter if the file completes.

int linesRead = 0;

const int SillyAmount = 1000000;

while (!EOF)
{
    text = ReadLine();
    // Do Some complicated processing with the text
    linesRead++;

    if (linesRead > SillyAmount)
        break;
}

Service conversation

In this example an object is gradually enhanced via service calls until the data is good enough to be processed later on.

int conversationLines = 10;

while (conversationLines > 0 && conversation.Status != Complete)
{
    conversation.Next();
    // Process conversation
    conversationLines--;    
}

Questions.

(1) Is there a design pattern or similar for this sort of thing?

(2) In the absence of (1) and given that you're artificially exiting a loop, could this be deemed a code smell?