Celsius, a London-based crypto lender, filed for bankruptcy protection roughly a month after halting withdrawals to stem losses from sharp declines in digital currency prices. Last month, Celsius investors told The Wall Street Journal they had no plans to put up more capital to save the company.

Across the market, other investors appear to be taking a similar sink-or-swim approach to their crypto startups, as the virtual currencies continue their downward vortex.

Sarah Guo, a board partner at Greylock Partners, said investors generally aren’t racing to bail out every troubled startup in their portfolio, “and that’s even more true in crypto.”

Easy money in recent years kept many unviable crypto startups afloat, Ms. Guo said. With cryptocurrencies crashing, investors now seem more willing to let these startups sink. “The market has gotten much quieter,” she said.

Greylock was an early investor in Coinbase Global Inc., a cryptocurrency exchange that went public last year. In May, Coinbase reported a first-quarter loss of $429.7 million. Greylock also has active investments in blockchain and Web3 startups.

In venture capital, early-stage investors tend to contribute to a startup’s subsequent fundraising efforts, as a way to underpin continued growth and increase the value of their equity stakes.

Between April and the end of June, there were 263 follow-on investing rounds for crypto-related startups worldwide, down from 307 over the previous three months, and 282 over the same period a year earlier, according to PitchBook Data Inc. The declines in crypto fundraising are part of a general slowdown in startup investing spanning sectors.

The total global dollar value of second-quarter followon deals for crypto and blockchain startups dropped to $5.6 billion, from $7 billion in the first quarter, though it remained above the $4.4 billion fetched over the same three months in 2021, PitchBook said.

To be sure, some crypto startups have continued to land outsize funding deals. Prime Trust, a startup that offers crypto custody and infrastructure services, said in late June it had closed a $107 million Series B round. Also in June, FalconX, a brokerage startup offering crypto derivatives trades to institutional investors, announced a $150 million Series D round. And Magic Eden, an NFT marketplace startup, closed a $130 million Series B round, co-led by Electric Capital and Greylock.

“Crypto has always been the purest form of capitalism,” said Satraj Bambra, managing partner at Round13 Digital Asset Fund, a Toronto-based investment firm that closed a $70 million fund in May to invest in cryptocurrency companies. “Whatever doesn’t work is going to get washed out, and money is going to go into new investments,” he said.

Several large investors have been hit hard by declining cryptocurrency values. Three Arrows Capital Ltd., a cryptocurrency hedge fund, last month was ordered by a court in the British Virgin Islands to liquidate its assets for failure to repay debts.

Vauld Group, a cryptocurrency lender backed by Peter Thiel’s Valar Ventures and Coinbase, this month filed for protection from creditors in Singapore, after recently pausing withdrawals and laying off 30% of its staff, The Wall Street Journal reported.

“This is a time to witness which investors truly have a conviction in cryptocurrency—who is a true believer in the vision versus what I would call the tourist,” said Mathias Schilling, a founding partner of San Francisco-based venture-capital firm Headline.

Some later-stage crypto funds are keeping an eye out for discounted shares in ailing crypto startup assets should investors start unloading stakes, Mr. Schilling said. That could include secondary sales of future equity or digital tokens, which crypto startups sell to investors in exchange for immediate cash, he said.

Headline itself has no investments in crypto startups as part of its core early-stage venture and venture growth funds, the firm says. Last year, it created a dedicated $80 million crypto seed fund with roughly 130 investments to date, Mr. Schilling said. The fund recently led a $3 million round for Alloy, a decentralized finance platform that lets users to send money anonymously over its blockchain.

Enzo Villani, founder and chief executive of Alpha Sigma Capital LLC, said he thinks Celsius won’t be the only firm to slide into insolvency. Though not an equity investor in Celsius, Alpha Sigma until last year held CEL tokens—Celsius’s unique digital currency used in transactions on its platform, which were issued to some investors in lieu of equity.

Recent turmoil “will cleanse the market,” Mr. Villani said, leaving those crypto companies that survive in a stronger position to move the industry forward.

Other investors have said occasional bailouts are the cost of doing business in an inherently risky market. But venture investors have come to the aid of crypto startups that lost millions to hackers.

Crypto platform Wormhole received an infusion of capital from owner Jump Trading LLC in February after hackers broke into the platform and stole $320 million. Game developer Sky Mavis Ltd. raised $150 million from investors to help reimburse victims of a March cyberattack targeting the online game “Axie Infinity.”

Louis Lehot, a partner at law firm Foley & Lardner LLP, said investors are demanding friendlier terms on crypto-startup funding deals to gird themselves against added risk. These can be in the form of side letters with added investor rights and protections, such as co-sale rights, which entitle holders of minority stakes to cash out if a majority shareholder abandons the startup.

Armed with these and other safeguards, Mr. Lehot said, many high-profile investors with dedicated crypto funds are circling for possible Series A investments in the coming weeks, “presumably to take advantage of investor-favorable valuations in the current environment.”