While this may cover many ways of overflow (from integer and counter all the way to record, I assume the Overflow in question is about floating point, which more precisely means over/underflow of the exponent.
The exact handling varies widely between compilers and machines. Fortran 77 did not make any assumptions here (AFAIK), it at all, it was expected that the program will be aborted like with any other machine error.
In general: Fortran is, much like Assembler, not a 'nanny' language, made to pamper every possible fault, but expects the programmer to write a program tailored to its data, not producing any error under normal condition. As a result, program abort is a sensible default solution.
Of course, it's always possible to add checks. Already early Fortran (no number) for the IBM 704 added the ability to check for conditions (ACCUMULATOR OVERFLOW, QUOTIENT OVERFLOW, and DIVIDE CHECK) after a calculation.
Over the years all modern compilers have added specific tools to handle such conditions, especially when IEEE float became a thing in the 1980s. For example Oracles's F77 compiler for SPARC and x86 may be told to not abort right away, but record 'flags' about operations. These can be tested when the programmer expects some error condition and is willing to handle it.
x = d_max_subnormal() / 2.0
ieeer = ieee_flags( 'get', 'exception', 'overflow', out )
IF ( out .eq. 'overflow') PRINT *,'overflow flag raised'
This is mainly done due performance reasons. Error checking costs time and Fortran users act usually at the top end of what's available in computing power, so any additional code is to be avoided.
Then again, Oracle F77 allows as well for generation of exceptions. It's a modern implementation, so it gets soft on anyone short of a real programmer. This means an exception handler can be added:
i = ieee_handler ('set', 'division', myhandler )
With IEEE FP rules became defined about what results of operation with not fitting values (*1) should be, enabling to continue operations after overflow even further.
Long story short: Check Machine and Compiler Manual in Operation.
*1 - Trying to avoid the word 'not numbers'