Let me help you. First question, NON PAYMENT of account balance will redirect accounts services, disconnect, and worst scenario is account termination.
Second and last question, NO. Once your account is terminated, your account will be endorse to the collection agency. The collection agency "by all means" will send A DEMAND LETTER to pay your obligation.
Depending on the amount, Globe or its collection agency will keep on sending demand letter for you to pay. If you disregard such demand, titigil na lang yan. NO CASE: NO CIVIL OR CRIMINAL ACTION
But, if you enter into PAYMENT ARRANGEMENT/INSTALLMENT OF PAYMENT AGREEMENT between you and the Globe collection agency, your FAILURE/NON COMPLIANCE in the said agreement is now a cause of action against you in filing a civil/criminal case in court. Dito, may case at pwde ka makulong.
Example: The collection agency will demand issuance of checks to secure the payment installment as agreed. If the checks bounce say lack of fund, and despite notice of dishonor, you did not cooperate or do something, the collection agency has a cause of action to file case against you under BP BLG. 22 (Bouncing Checks Law) dito may kaso at kulong.
To summarize, if possible you settle your obligation, although di ka makukulong pero BLACKLISTED ka naman sa Globe then your name will be included in the database Credit Information System, so most probably once you apply for loan or credit card, denied ka na agad.