A points deduction means that Southend sit on minus one after six games of the National League season, and their lot worsened when Louis Dennis scored for the hosts after 18 minutes.
Michael Cheek doubled the lead in the 55th minute as Bromley pulled clear of the relegation places.
A consolation goal scored a minute later by Noor Husin ultimately proved in vain as Southend finished the day six points from safety.
HM Revenue & Customs (HMRC) has issued a winding-up petition.
A judge in a specialist court was told on Wednesday that the sale of the National League club was in progress.
Judge Sally Barber, who oversaw an Insolvency and Companies Court hearing at the Rolls Building in central London, said the case would be reconsidered in six weeks.
She was told by Southend chairman Ron Martin that more time was needed to complete the sale of the club and clear the debt.
Another judge had adjourned a hearing in May after being told that the sale of the National League club was under way. The size of the debt emerged at the hearing in May.
Martin represented the club at Wednesday’s hearing and he told Judge Barber: “We are seeking an adjournment for 42 days to complete the sale.”
HMRC has issued a number of winding-up petitions against Southend over unpaid tax in recent years.
Southend, who dropped out of the Football League at the end of the 2020/21 season, featured in an Insolvency and Companies Court hearing in March, after HMRC issued an earlier winding-up petition over unpaid tax. Another judge heard how that debt had been cleared.
Despite the on-going financial issues, the Shrimpers finished eighth last season – just missing out on a place in the National League play-offs.