She thought she was early for her June eviction hearing. Minutes later, she learned that her landlord had already won the case. She is appealing the decision next month, but if she loses Ms. Mitchell could be kicked out of her home of 14 years because of the rent payments she has missed during the pandemic after losing her job.

“The fight started when I said ‘Can you have a little more compassion,’” said Ms. Mitchell.

With expanded unemployment benefits and a federal eviction moratorium covering millions of apartments both expiring Friday, more than 11 million Americans could be served with eviction papers over the next four months, according to global advisory firm Stout Risius Ross, LLC, which analyzed Census data on unpaid rent.

Houston is expected to suffer many more evictions than most major cities. That is because unlike in New York, San Francisco and even other cities in Texas, Houston has stopped providing protections at the local level, after a statewide eviction moratorium expired in May.

Tiffany Thomas, a Houston councilmember, said the city is counting on more rental assistance from Congress to stop the wave of new filings. But hundreds of Houston renters not covered under the federal measure have already been served with eviction papers each week since the state’s eviction protection expired.

“This thing is already out of the gate and we’re already trying to put the water back in.” Ms. Thomas said.

Ms. Thomas represents parts of Southwest Houston, the largely Hispanic and Black section where Ms. Mitchell lives and one of the city’s most vulnerable neighborhoods to mass evictions. Its major thoroughfares are dense with working-class apartment complexes, and it has the highest renter population in the city, according to an analysis from Houston-based data science firm January Advisors.

The area has seen more eviction filings than most other parts of town over the past several weeks. Legal aid attorneys say they have noticed long lines at courthouses, sometimes people standing shoulder-to-shoulder.

Across Houston, eviction filings more than doubled in June compared with May, according to Princeton University’s Eviction Lab, which tracks evictions in several U.S. cities. The 2,483 evictions filed in Houston last month are fewer than what the courts typically see in June. But with courts just now processing cases again, and the expiration of the federal eviction moratorium, housing attorneys and tenant advocates expect evictions could soon surpass historical averages.

Houston’s mayor, Sylvester Turner, hasn’t put an extended eviction moratorium on his agenda and has instead said the city needs more federal financial assistance to address the problem. In April, Mr. Turner signed a letter asking local judges to halt eviction proceedings until August.

Evictions in Houston are rising as Covid-19 cases there are also surging. On July 17, Harris County, which includes Houston, recorded its highest seven-day average for new cases during the pandemic, with 1,650 confirmed cases, according to the data from the Texas Department of State Health Services. Southwest Houston ZIP Codes have some of the highest case counts in the entire city.

Advocates say eviction is a risk factor for virus transmission because it leads to overcrowding, as the evicted then turn to friends or family for temporary accommodations, causing people to double up in small apartments. The Centers for Disease Control and Prevention has cited “poverty and crowding” as one of the top significant risk factors for severe Covid-19 illness.

Some policy makers and landlords remain skeptical that extended eviction bans will solve the problems Houston’s renters are facing. They argue that in addition to hitting the pockets of property owners, eviction delays don’t address the issue of unpaid rent for tenants.

“You’re just kicking the can down the road and just letting the problem grow bigger and bigger for the resident,” said John Boriack, president of landlord Veritas Equity Management and president-elect of the Houston Apartment Association, a trade group.

The Houston Apartment Association has been lobbying both local and federal government to provide more direct financial assistance to renters, Mr. Boriack said.

Greg Travis, a local City Council member who said he represents Houston’s wealthiest district, said that instead of banning evictions across the board, the courts are best-equipped to deal with the varying intricacies of eviction matters. “Every situation is unique. Not every eviction is because you’re not paying rent,” Mr. Travis said.

Most tenants don’t have legal representation in eviction proceedings and don’t file appeals of their evictions. After receiving an eviction notice, tenants often decide to leave their homes before even going to their own eviction hearing, tenant attorneys said. That is partly because in Houston there is no legal defense for unpaid rent. Defendant tenants who can’t pay at least one month’s rent into the court registry automatically lose.

“These cases move very fast,” said Houston attorney Velimir Rasic, who is representing Ms. Mitchell in her eviction case. “If you don’t appeal within five days there is no further recourse.”

To protect more tenants from evictions during the pandemic, some cities have chosen to use funding from the federal coronavirus stimulus to pay for legal representation. Those cities include Atlanta, Chicago, Baltimore and Detroit.

Ms. Mitchell, who has applied for unemployment benefits but has yet to receive them, appealed her eviction by asking family to help her pay the required one month’s rent into the court registry. There is no date set for her hearing yet, but it will likely occur sometime next month.

Although there is typically no defense for unpaid rent in Texas, Mr. Rasic plans to argue that Ms. Mitchell shouldn’t be evicted because of “impossibility of performance” during the pandemic.

“You’re very limited in how you can fight these cases,” Mr. Rasic said of the legal approach. “It’s still very new. I don’t know how successful it will be. But it’s the best we have right now.”

Write to Will Parker at will.parker@wsj.com