You couldn’t just fail to that state (it’d be inappropriate for its primary use-case), as long as there’s some way to get there.
If you want to know where to start, search GitHub for 'KaveriPI', if you unpack AMD BIOSDBG.EXE you can find a complete list of processor registers. This is all from 2015 but the PSP is documented in there.
There's also a Microsoft Access database which has all the JTAG registers, but I don't have the time to decode the meaning of the fields... It is likely that things have changed since then but it still might be enough for a start.
Should the JTAG interface be protected then some kind of laser(?) fault injection might be required to open it up. I guest some of the eFuse bits can be overwritten, maybe there's a combination which can remove the lock. An innovative recycling company could work on making a jig to automate this somehow...
Some PSP JTAG stuff here (publicly available material from GitHub in 2015, fair use applies): 41469,3529,164000,164999,"SMU_PSP_efuse_ovr_tried",,1,0,0,0,50,"0000",0, 41470,3529,164000,164999,"SMU_PSP_FRA_pass_ld_err",,1,1,1,0,50,"0001",0, 41471,3529,164000,164999,"SMU_PSP_FRA_pass_ld_cor",,1,2,2,0,50,"0002",0, 41472,3529,164000,164999,"SMU_PSP_efuse_pdmb_aes_dis",,1,3,3,0,50,"0003",0, 41473,3529,164000,164999,"SMU_PSP_efuse_pcpu_dis",,1,4,4,0,50,"0004",0, 41474,3529,164000,164999,"SMU_PSP_efuse_ccp_cyph_dis",,1,5,5,0,50,"0005",0, 41475,3529,164000,164999,"SMU_PSP_efuse_FRA_en",,1,6,6,0,50,"0006",0, 41477,3529,164000,164999,"SMU_PSP_efuse_proto",,1,7,7,0,50,"0007",0, 41478,3529,164000,164999,"SMU_PSP_efuse_secure",,1,8,8,0,50,"0008",0, 41552,2352,164000,164999,"SMU_PSP_hard_resetb",,1,31,31,0,50,"101F",0, 41553,2352,164000,164999,"SMU_PSP_early_resetb",,1,30,30,0,50,"101E",0, 41554,2352,164000,164999,"SMU_PSP_slv_mbus2_reset",,1,29,29,0,50,"101D",0, 41555,2352,164000,164999,"PSP_SCAN_MODE_STICKY",,1,28,28,0,50,"101C",0, 41568,2352,164000,164999,"PSP_AEB_307_PCPU_RST_DLY_TDR_en_pclk",,1,15,15,0,50,"100F",0, 41569,2352,164000,164999,"PSP_AEB_304_PCPU_FORCE_rst_en_pclk",,1,14,14,0,50,"100E",0, 41579,2352,164000,164999,"PSP_Resetn",,1,8,8,0,50,"1008",0, 43605,555,164000,164999,"PSP_ENABLE_SPARE",,0,1,1,0,50,"0001",0, 43642,555,164000,164999,"PSP_SPARE",,0,7,14,0,50,"0007",0,
https://pbs.twimg.com/media/D3jU2ZuU8AE_JgS?format=jpg&name=...
AMD is unlikely to sue anyone trying to reverse engineer the JTAG interface, especially if it's for an open source project to unbrick CPUs! If they do the EFF is very likely to step in and defend you.
The SMC ROM contains code to initialize the hardware before the PCIe links are brought up. One of the first things the SMC does after boot is read out the eFuse contents and program various 'write once' lockdown registers which are used to disable features within the chip. Once these registers have been written to they cannot be modified until a hard reset occurs. So you write to these before the SMU gets a chance to. Or you can halt the SMC itself, then write whatever registers you want and reboot it as nothing ever happened. That way you can override many of the eFuse related settings.
The above techniques might also work on PSP based CPUs/GPUs - so you need to access the JTAG interface ASAP after bringing the chip out of reset. I'm unsure if the SMC is still present on the PSP-based CPUs and GPUs, as I don't have any spare to test.