My interpretation of this statement is that abundant availability of liquidity and funding will push banks to adopt reckless strategies, especially in terms of maturity transformation $-$ i.e. borrowing short-term and lending long-term to earn a spread $-$, leaving them exposed to a sudden liquidity impact which could dry their short-term financing sources and plunge them into a liquidity crisis.
Take for example the years preceding the 2008-2009 Financial Crisis. At the start of the 2000's, commercial and investment banks became more and more dependent on wholesale funding, provided primarily by institutional investors (pension funds, insurance companies, investment funds, etc.). Compared to the relative stickiness of retail deposits, wholesale liquidity tends to be short-term, highly volatile and sensitive to the credit profile of the borrower: as soon as doubts arise concerning the solvability or liquidity position of the borrower, participants in the wholesale funding market might abruptly withdrawn, leaving the borrower exposed to a liquidity shortage.
Banks dependence on the wholesale funding market kept increasing during the 2000's, as it was a cheap financing source allowing them to earn profitable spreads between their short-term borrowing and their long-term lending. One of the offspring of this trend were Structured Investment Vehicles (SIV): you might have heard about Mortgage Backed Securities (MBS) and Collateralized Debt Obligations (CDO) and how they contributed to the Financial Crisis; well, large part of their impact was through the SIV channel.
A SIV is similar to a MBS or a CDO: instead of mortgages, SIV package together other MBSs and CDOs into a legal shell; the shell then issues short-term notes (commercial paper) to investors, which interest is paid through the coupons received from the underlying MBSs and CDOs. Because maturities were very short, the SIV required refinancing very regularly: new short-term notes would be issued, which would allow to repay preceding investors. In case of financing gaps, the bank backing the SIV $-$ i.e. setting up and managing the SIV $-$ would be standing to refinance the structure and repay the notes' principal.
As you might have guessed, during the Crisis, uncertainty about the liquidity and solvability position of some banks led institutional investors to withdrawn from the wholesale funding market, and one consequence was that banks were left exposed to their off-balance sheet SIV and the resulting financing needs; some of these institutions (Bear Stearns, Lehman Brothers) didn't manage to survive the crisis and were indeed "killed [...] slowly and surely".