Like most corporate debt, the debtor must service the debt repayment schedules while following financial covenants (addition rules on performance ratios). If debtor fails to make payment or breaches covenants, it can lead to a technical default.
In this case, most of Twitter’s LBO debt haven’t been syndicated (ie. The banks still hold them and haven’t securitized them to be sold to other investors.) Twitter no longer has a credit rating (Moody dropped them in Nov, S&P dropped them in Dec; both citing insufficient information to assess credit risk). Without a credit rating, most bond investors simply won’t buy the debt because it wouldn’t meet their investment guidelines.
Also, there can absolutely be margin calls on equity holders of private equity if their stakes were financed on margin. ie. If a hedge fund (most are leveraged at least 100% for financial reasons) chipped in, their margin creditor (ie their prime broker) can absolutely request the fund to post more collateral.